It seems like art made of wax would be very vulnerable to heat, but it takes a lot more than a warm room to melt wax. Unless your house is hot enough that your candles are drooping an encaustic artwork should hold up fine. Direct sun or time in a hot car might be disastrous but that kind of torture will do in other media as well.
If a painting has gotten dusty try blowing the dust away first, if it still needs dusting do it very lightly with a very soft cloth or feathers and only rarely. The wax surface can scratch or get shiny with rubbing. I intentionally buff some of my paintings for a high gloss that intensifies the colors, others I leave with a velvety unpolished surface. Don’t use any cleaners on the surface and feel free to contact me if you need advice on a specific problem.
The wax surface is somewhat soft and can be scratched or the edges chipped. So carry paintings by their frames or by the hanging wires so that you don’t touch the face. If you need to protect a painting in transit a layer of wax paper secured so it doesn’t slide around can help.
For more information on making and caring for encaustics see this FAQ at R&F Handmade Paints.