I use this one. When you first get it, take it outside, plug it in, and run it on high to get rid of fumes. After that, set it to the temperature you want, and run it on LOW. IT should keep the room warm. The outside does not get hot when you run it on low, not at all. They can climb on it and it won't hurt them.

If you don't like this one, you can do a search on cool touch fan forced digital heaters and see what else is out there. This is a good price. Last year I paid 15 dollars more for this model.