Hello Todigman,
Two words come to my mind immediately: FIRE HAZARD.
However, an open flame such as a small propane heater will produce CO2. Keep a pot of water simmering on it to restore humidity. If you fall asleep in there you might not wake up. If the flame goes out unburned propane will kill your plants. If a light switch or timer arcs while the shed is filled with raw propane gas, your shed will explode. If you can avoid all that your plants will grow really fast.
I'm sure there are safer methods but they're expensive also. A heated vented green house? A bottled CO2 system? I'm sure someone can come up with a better idea.
Good Luck,
Ken

Is the shed close enough to the house that you could run a small 4 inch household insulated ducting tube to it? You can run the intake from a nearby window, doorway, vent, etc. It would just need a small inline fan to draw the air into the shed.

Also, what's the daytime and night time temps your dealing with (both inside and outside of the shed)? I can think of a few alternatives but temp, location, resources all play a part in practical functionality. Is the shed see-through (using natural light) or are you using artificial light that gives off heat? If so, then cool air can be drawn in directly into the light source (reverse light ventilation) and the lights would heat the air coming in. If not, does the natural light (sun) warm the shed during the day through solar energy?

the byproduct of fermentaion is CO2. why not put some yeast in sugar water under a fan. Under a fan as CO2 is heavier than air and thus won't float out of the bucket, pot, what not.

I have seen the videos on you tube that show making a Yeast (co2) generator also. Though I am not sure I can say I am impressed for a couple of reasons. Not that it doesn't work, I fully believe it does. But I think it would be more trouble than it's worth in the long run. First off, I'm just not sure exactly how much co2 is created per volume of yeast and sugar (in the water). Depending on the size of the shed and number of plants, it may take a large volume of fermenting liquid to create enough co2 to be effective. That could wind up being expensive in the long run. Also, I used to make my own beer and I remember the smell of the fermenting yeast. There has to be other byproducts given off other than just co2, and at this point I don't know what that would do to the plants.

I had plans to build a small propane heater to heat a makeshift greenhouse last winter. I wasn't planing to use it to replace co2 (though it would), I just needed it for heat. The design I have wouldn't fire hazard, the worst that would happen is that a real strong wind might blow it out. But my makeshift greenhouse was well ventilated, no buildup of gasses would be possible. The plants would just wind up being cold the rest of that night. But our coldest nights range in the low 30's, so I only need to heat it about 20 degrees.

you can also just add flour to water and yeast will naturally inoculate the formula to yield the same results. you just have to skim the liquid off the top every few days and remember to feed it more flour. (think sour dough bread)I don't think there are any bad gases released in the process. Remember a lot of bread has been made this way. I do agree, however, that I have no idea how much of this yeast mixture would be required.

I wasn't thinking that there was toxic gasses given off, I know that yeast is used in all sorts of food and drink. Just that whatever is given off may build up to toxic levels for the plants. To much of a good thing is not always good. Even too much co2 is damaging to plants. Also any element in a nutrient solution, if in excess is not healthy and can become toxic to the plants. I am also half to wonder if there would wind up being any type of film that may settle on the foliage that could hinder plant transpiration.

I haven't seen or herd of it being used for generating co2 for plants (not that I've looked hard). The only way of finding out if it would be efficient that I can tell is to do some test. I would build a small scale test box with a known inside square footage. Use a co2 meters/sensor to measure the any increase in co2 PPM (with different levels of product in a given amount of liquid). Then with that data in hand I would introduce some plants to the setup, and again measure the co2 PPM's.

I would also introduce a few pains of "clean" glass to see if any film builds up on it over time. Also I would want to test how long the mixture will give off the desired amounts of co2. So once I had reached reasonable co2 levels, I would do an experiment testing the daily PPM's to see when the co2 start to drop off, and how fast (keeping logs for all experiments). Once I had all that data then I could figure out the size of the yeast co2 generator I would need for a larger scale enclosure (and plants planed). That would also give me some idea of if it would be cost effective in the long run.

As I understand it the PPM levels for co2 and healthy plant growth can vary a widely. With CO2 levels of below 200 ppm will generally cease to grow or produce, and levels above 2000 ppm reaching toxicity levels for plants. Although PPM levels very by location, climate, and season, Carbon dioxide (CO2) is present at a concentration of approximate average is 350 ppm in the atmosphere. CO2 is heavier than oxygen and will also displace the O2 required by both plants and humans (air circulation would be recommended). OSHA's maximum allowable levels for human exposure is 5000 PPM.

Supplemental Carbon Dioxide
Do-It-Yourself Carbon Dioxide Injection (note: this article is referring to co2 for aquariums)

I could swear I had a couple more links, but cant find them right now.

I sense a logic train passing by the station here, re: yeast and CO2.

Let's look at this equation, shall we?

Sugar -> Yeast -> CO2 -> Plants -> Photosynthesis -> Sugars

So even if it was 100% efficient, all you're doing is moving store-bought sugars into the sugars in your plants, esp. when the plants start metabolizing. Of course, it'll be nowhere close to 100% efficient. Plus, you'll have to deal with cleaning out yeast detritus and all of that sort of stuff.

The typical way commercial growers deal with this, if they have to, is with a CO2 generator. That's basically a propane tank with a pilot light. If you have a small enclosed space, I would not use one inside; rather, I'd have it outside with ducting to the inside.

Note that enclosed spaces have their own problems. If there's any sort of flame and any sort of ductless or open-flame source of heat or CO2, you risk carbon monoxide buildup. From your perspective, that's bad, and it hurts plants too (just not as much as it hurts you). Unburned propane is also bad for plants. But the worst one is ethylene gas. That can come from the propane, but most commonly it comes from the plants themselves -- whether or not you're burning anything for heat or CO2. If you have poor air exchange in your building, ethylene can build up to problematic levels, causing leaf and flower malformation. So no matter what, you need at least *some* air exchange.

You can skip CO2 generators altogether and focus only on air exchange if you want. This is usually done through a countercurrent heat exchanger. That is, to say, you have air going out in close contact with air going in, with the air travelling in opposite directions. An infinitely long or infinitely conductive countercurrent heat exchanger with zero viscosity losses is 100% efficient -- that is, to say, you lose none of your indoor heat while replacing the inside air with outside air. Naturally, you can't achieve 100% efficiency in the real world, but you can usually do a pretty good job. Basically, you need two long, insulated metal ducts of some sort (they don't need to be very large, but they need to be long!) in contact with each other (the more the surface area, the better), and you need to wrap good insulation around the whole thing. You can then either force air through it or rely on a wind scoop or other passive system to drive it.