I use those radiant oil heaters in my 4x8' boxes. They work perfectly, but they take up a lot of floor space once you contain them to keep the tortoises from touching them.
I'd use the Kane heat mat/radiant heat panel combo in the 4x4'.
These might offer some reference material:
http://www.tortoiseforum.org/threads/another-night-box-thread.88966/
http://www.tortoiseforum.org/threads/my-best-night-box-design-yet.66867/
http://www.tortoiseforum.org/threads/double-door-night-box.129054/
Even more important than which heating strategy you go with, is the insulation and silicone sealing. If you don't do those two steps right then the heating strategy isn't going to matter much.
I am going to follow your insulation recommendations. I had a set back last weekend and could not begin construction but I was able to buy everything.
Wish me luck. I'm dreading this but if this turns out good I will be so happy! Figured I'd take pictures as I go. Wanted to ask about heating. Panel or radiator? I found this radiator for only $30 on Amazon. Says it will heat 70 sqft. I'm doing a 4x4'. Think it will work?
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I am going to follow your insulation recommendations. I had a set back last weekend and could not begin construction but I was able to buy everything.