For moderately cold weather (above 0F) I have liner gloves made by OR, plus Sno-Claws made by Heat Factory that look like a mitten with a separate index finger. They have a pocket for a little chemical heat pack on the back, which I've never used. I also carry a spare pair of wool gloves and lightweight mitt shells for emergency use.

If it's really cold, I would buy a big pair of insulated mitts, preferably with a removeable liner.

However, for working around a stove, I think I'm going to pick up some leather work gloves, like the ones Kinco makes. You can see them on their insulated Kinco gloves.

Some of the Canadian guys who hot tent and have fires wear leather gloves with liners to prevent exactly what you are talking about-burning or melting a synthetic glove. The last thing you want is to melt a glove to your hand out in the wild and a leather glove will prevent that.