I don't think heat would be such a big problem. A 4 x 5 has 20 square inches. A 35mm slide has 1.5 square inches. So the heat will be distributed over 13 times more area than for a 35mm slide. A typical slide projector uses a 300 watt halogen lamp. Assuming you don't need to cover a larger screen than say, 4 by 6 feet, 300 watts should do the job and the slides should run pretty cool. With the right screen, you can even go larger.
I wonder if some of those flat plastic fresnel-type magnifiers sold in places like Walgreen's, etc., could serve as the condenser? Maybe if stacked up. Otherwise, the lenses from a condenser enlarger should be good. You could put a 300 watt projector bulb behind it. ELH for normal brightness; ENG for extra bright. Don't forget the fan. I'd use a muffin fan. These are common in electronic equipment, and you can get them in electronic supply houses and online from places like Mouser.