Yes, that would help speed up the composting. I'd aim for 125-130 degrees F.

adding in some molasses with your watering regimen might assist in boosting up the microbe population as well.

The heat generated in a compost pile is the result of bacterial activity. Maybe placing the compost near and external heat source would keep the pile warm enough during cold weather to keep those bacteria warm enough to keep working, maybe not.

Most winters, here in Michigan, my 4 x 4 x 4 compost piles are being worked on all winter long without the need for an outside heat source, but smaller piles frequently cool down too much for the bacteria top keep working. If your heat source is already there it may be worth trying, but if you need to set up a heat source to do this it most likely would not be worthwhile.

kimmq is kimmsr

Perhaps you should consider keeping worms at room temp,they work great for small amounts of material and IMO the finished product is far better for plants.

Compost does have insects and may create some odor in a closed space even if the pile is well managed. That's why we typically don't compost inside. If I had a greenhouse I'd probably have a pile in there all winter though.

You might also look into Bokashi composting for your kitchen scraps. It can speed things up considerably without the problems conventional composting might cause indoors.

Another idea is to lay those materials down as mulch right on your beds, aka sheet composting. This can actually benefit soil more than adding finished compost, as the decomposition process itself has beneficial effects on the soil food web.

This is an old thread and I am very late to the party but I am more than a little amazed that anyone who understands composting thinks applying artificial heat (heat from an outside source) is going to help or speed up the process. The ONLY heat that is of benefit to and will expedite the composting process is the internal heat created by the microorganisms populating the compost as they consume and digest the organic matter ingredients. If these organisms are not actively producing the heat themselves - eg, a hot compost pile - then applied artificial heat is not going to help. Heat is a byproduct of the composting process and internal compost heat/temperatures are not the same as applied heat from an outside source. You cannot substitute one for the other. They are not equivalent.

An active, hot compost will work all through the winter and cold weather but it will require attention - protection from excess water but not allowed to dry out. It also needs to be turned regularly to introduce necessary oxygen. Covering with a tarp or horticultural fleece in winter can help maintain the exterior temperature from extremes but it is a waste of time and effort (and electricity) to attempt to heat up the interior in the mistaken belief it will speed things up. It will not.

OP's need to compost a small batch in cold weather is shared by many that don't have ample resources for material. As previously pointed out, composting creates a few odors so best done outdoors. I would suggest insulation. One hack that comes to mind is chest food freezer or an upright fridge lying on it's back. More conventional would be cardboard which could be used as carbon after starting to disintegrate. Dry leaves covering heap acts as insulation whereas wetting outside has a cooling effect form evaporation.