With stovetop cooking, is there a way to retain heat but let moisture escape? Example: I made mulled wine and want to keep it warm on the stovetop. If I put the lid on, it will get too hot; if I take the lid off, the alcohol and flavors might evaporate. So, I want to keep the moisture in, but let the heat escape.

Opposite example: I am cooking onions on the slow cooker. If I put the lid on, the onions will get mushy/soggy. If I take the lid off, it takes too long to reach cooking temperature. So, I want to let the moisture out, but keep the heat in.

How can I control heat and moisture separately? Does opening the lid partway accomplish anything?

(Note: maybe these are not the best examples but just want to illustrate.)
You don't really have much control, at least not very directly like turning a knob. You can control it a bit by your choice of cookware - a thin-walled pot which is relatively high in comparison to its width will dissipate heat more than a squat, thick-walled one of some non-conductive material like cast iron or ceramics. If you want more moisture escaping, go for wide vessels and don't heap your food in them, place it in a single layer. 

Another option is to cook food in an oven, which allows it to be heated slowly, but the moisture is not as trapped as it would be in a closed pot, so the food doesn't become soggy. 

Your examples here are not generally tackled by separate moisture/heat control, though. For the mulled wine, anything that escapes with the lid off will also escape with the lid on. People usually simply reduce the temperature and keep the lid on, to save energy, but keeping it with the lid off doesn't make a difference. For the onions, if you want them done quickly, you shouldn't be making them in the slow cooker at all, but shallow frying them in a pan. I know you said these are examples for illustration, but I suppose that for any other examples you might come up with, there are already established ways to do them and your problem might be arising from not following those.