Damp towel can be helpful. Just be careful those warming drawers can actually be too warm. You don’t actually want more than 100 degrees and better in the 70 – 95 zone. Alternatives include a warm spot in the house and and many place in microwave with a steamy cup of water. You get moisture and warmth in that version.
My house is pretty chilly in the winter (67 degrees) so I’m wondering if I can use the warming drawer in the oven to get it to rise? I’m just worried that it will dry out the top of the dough. Can I put a piece of parchment over the dough and then a damp towel on top of that and put it in the warmer on low?