Hitler used a heater in a nylon tent. You don't want to be like Hitler, do you?
Good grief. I've yet to see a three season tent that'd present ANY risk of CO or CO2 poisoning from a heater. There's usually so much mesh in the tent body that even a light wind will blow through the whole tent. Fire hazard is a risk, especially in a small tent, which is what several people have mentioned.
In my ultra-dangerous use of a Big Buddy heater inside a large tent, I put the heater on a steel pan, make sure nothing is within 3' of it, leave the 20 lb propane tank outside, and don't sleep with the heater on. I'd write of the military's death defying, decades long use of gasoline/diesel/coal/wood fueled stoves inside tents, but I think it may be too scary for some members.
For the record, I don't believe the OP wants to heat his tent with a lump of plutonium, either.