I can't say anything about wild fire conditions, but even a decent hobbyist drone will not have problems with thermals in calm weather or slight winds. A commercial drone will be even better.

Unfortunately the thermals rising from large fires can be ridiculously powerful.

From http://en.wikipedia.org/wiki/Pyrocumulonimbus_cloud:

"On the 18 of January 2003, a supercell thunderstorm formed from a pyrocumulonimbus cloud associated with a severe wildfire, during the 2003 Canberra bushfires in Canberra, Australia. The supercell resulted in a huge fire tornado, rated at EF3 on the fujita scale, the first confirmed violent fire tornado. The tornado and associated fire killed 4 people and injured 492."

Now I know the third movie in the Sharknado series, Sharknado vs Firenado.

That is an interesting link. Reading about the Australian fires an interesting question comes to mind which is this, "If we engaged these fires at the outset with a constant suppression/extinguishing scheme, would they still get to the size and ferocity that they do today?" that is something I don't know. CalFire jumps on fires pretty quickly to keep them under control, especially near structures, and those fires then evolve slowly. Unlike say the Yellowstone fire a decade or so ago which was left to burn 'naturally' and it got quite large.

The generally accepted idea of Eucalyptus fires is that you need to manage the fuel load on the ground. Regular burning off, maintenance of fire trails, clearing undergrowth around populated areas etc. is really the only way to control a plant that uses fire as part of it's reproductive cycle. Ignoring it for 10 years inevitably sets up a literally deadly fuel load which will be completely uncontrollable if it starts burning.

I grew up in the Australian bush, and it, like the Californian Eucalypt forests, is prone to burn at the slightest provocation. Add dry, windy conditions and it's a recipe for disaster.