Is it technically possible to have nuclear-powered hot-air balloons?
Most likely no.

RTG does not have enough power. The burner of the hot air balloon requires 2 to 4 MW of power (here) so you need at least 4 tonnes of Pu to produce that (2000,0000 / 500 = 4000 Kg), assuming 500 W per kg (0.5 W/mg). From the source, a moderate size balloon can lift few hundred kilograms at most.

The true nuclear reactors provide much more power, but they are heavy. Hyperion, for instance, provides 25 MW and weighs 50 tons, so performance per kg is even lower. It could power a cluster of say five balloons, but they would not be able to lift 10 tonnes each. 

From the other side, nuclear reactors are probably not optimised for the minimal weight, assuming that just a heat output is required. They are built to match different requirements, so some specially built device may be capable of lifting the balloon.

Lockheed Martin is developing a very promising device.