>>What types of material do you use?
Plywood, MDO (Medium Density Overlay), Melamine
>>What can you build with that will still allow belly heat from a heat pad or flex-watt tape and not damage the material?
Anything. Chris Harper has a good discusssion about this in response to a question from steve1488. Just cut a hole in the wood bottom of the cage and cover the entire bottom with a relatively thin sheet of expanded PVC, glass, or acrylic. Attach the heat tape to the PVCX. Caulk around the edges and you're good to go...
>>And are there any sites or plans that people are willing to share?
This question always amuses me for some reason... A cage is a box with five sides. How much of a plan do you need?!?
I suspect that what most people are really looking for are construction techniques. Here's what I'd suggest: figure out how big a cage you want to make. Let's assume it's going to be three-feet wide, two-feet deep, and 18 inches tall. You'll make it out of 3/4" thick material.
To make a cage with sliding bypass doors, you'll need the following pieces:
1 Back: Should be WxH in size. For our theoretical cage, that's 36 inches by 18 inches.
2 Sides: Should be H x (D-3/4) in size. For our theoretical cage, that's 18 inches by 23 1/4 inches.
1 Top, 1 Bottom: Should be (W - (2*3/4)) x (D-3/4) inches in size. For our theoretical cage, that's 34 1/2 x 23 1/4 inches.
2 Door Mounting Rails: Should be (W - (2*3/4)) inches by a couple of inches. For our theoretical cage, thats 34 1/2 by 2 inches.
The first thing to do is buy some iron-on edge-banding and attach it to any edges that will be visible. Trim to size using an edge trimmer (e.g. Item #99K40.01 at leevalley.com). You can do this after the cage is assembled, but it's easier if you do it now. Do the front edge of the top and bottom, all four edges of the back, and three edges of the sides (everything except the back edge).
Screw the Top and Bottom into the sides. Screw through the side pieces and into the top/bottom. This should give you a four sided box. Attach the back to this box with screws. You should now have a five-sided box. Take the two rails and mount them vertically across the opening; one across the top, one across the bottom. Screw through the sides and into the rails.
But some plastic sliding glass track from Rockler.com. Glue it to the edges of the rails. Buy some glass and insert it into the track. Buy some door pulls from wwhardware.com. Peel off the backing and attach them to the glass. Congratulations, you're done!