Now, having said that, keep in mind two things: One, the BlackCat does produce heat, therefore you don't want to put it where it might get covered by a jacket or unrolled sleeping bag. It won't ignite things quickly, but they will melt and could in time catch fire. Common sense is the key here. Two, because the BlackCat is burning propane, you will need some ventilation. Coleman recommends a six-inch opening somewhere near the BlackCat for safe usage.
Still, having said all that, the BlackCat is a reasonable thing to use in a tent, particularly a roomy one. In a little two-person tent? Still OK, but just be prudent.