Heather.... well, I wouldn't dry most herbs at 110º. The one problem I see with your greenhouse would be #1. Light, most herbs should be dried in the dark. #2. Humidity. Humidity makes for rotting before drying. If you have an a/c, indoors might be better.
Herb oils are a problem, what herb oils do you want to make? Fungus and other bad buggies tend to form in the oil and make it unsafe to eat.
You can try online, the Sunshine Bottle company. I like them.

Really? I had no idea about herb oils being a problem. Here is the recipe I was going to follow. What do you think?

Here is a link that might be useful: Making Herb Vinegars and Oils

You weren't going to ingest that oil, were you? I am pretty darn sure that was for external use only. Leave some olive oil in the sun for two weeks.... just a small sample, smell it and tell me you want to eat that! :o)

That oil is for ingesting. Not sure I'd want to, but it says it's for sauteing meat, etc.

Okay...reread it... the vinegar is a fungicide, but as a winemaker, I would THINK that if there is something in there fermentable, it'd turn it into vinegar too.... but I could be wrong. I just don't want to recommend herbal oils and have somebody get salmonella or something.

I have to admit that I've never done it, but isn't the oil heated along with the herbs to just not quite boiling, then the oil finely strained to remove any plant matter? If so, I would think that would take care of any pathogens. Then I would keep the oil refrigerated.

IE; drying herbs, it depends on what you are using the herb for. If you are using them medicinally, you want to retain as much of the essential properties as possible, so drying under open shade with good ventilation, and spreading out the herbal material is important, especially under humid conditions. An unventilated greenhouse in summer would be too hot, and evaporate many of the important medicinal components. For medicinals, its also important to tincture or store the dried material ASAP after drying, to avoid further degradation. Properly dried herbs should be a nice dark green color, smell green and lovely...the dried herbs in stores are usually poor in comparison.

If you are using hebs for culinary purpose, all the above holds true for best flavor, but you have a bit more leeway, they'll still have flavor, but you may need to use more.

For herbal oils, you want your herbs to be thoroughly well-dried to reduce pathogens. garlic is a nice addition as well, for flavor, but also to kill bad buggies.

Hope this helps!