I can't disagree with anything here as I know nothing about this. I just ponder your question.
What is a flame here? Could it be a jet of air heated electrically to 500oC? In that case wouldn't a whole room full of air at the same temperature have more heat to raise the temperature of the cactus to 500oC and be more likely to ignite it?
Do you think that the flame having some active burning actually has something more than temperature that it can pass on to the cactus?
It might depend on what part of the flame touches the cactus. I'd guess a living flame has significant variation in temperature. The unburnt fuel & air mixture would be cool, then getting warmed by the flame to combustion temperature, it starts to burn and gets rapidly hotter until it has all reacted. Then it will start to cool as heat is lost to the surroundings and the incoming unburnt gas.
I'd have thought the trouble with the hottest part of the flame might be that there was no oxygen left to burn the cactus. So you could use it to heat the cactus, then you'd have to move it away to let surrounding air get to the cactus. Then the cactus would have to heat up that air and cool down itself a bit. I wonder if the cactus burns when it is at 500 oC and the air is still 20oC, or whether you need both air and cactus to be over 500oC? But the jet of electrically heated air would have the advantage that it still contained lots of oxygen.
I don't know much about cacti (catuses?) but they seem a funny thing to burn. I thought they were full of water. So would you have to wait until the water had all boiled away before the cactus could warm above 500oC and catch fire. Some things, when you light them, they burn for a bit and then go out. Damp wood for example. So I wonder if water is the problem? The wood gets heated by a flame, say, then catches fire and burns a bit. That presumably makes more heat to heat up more of the wood, so that it catches fire too, in a sort of chain reaction. But if there is a lot of water in the wood, the heat generated is used up boiling off the water and there is not enough left to get the next bit of wood hot enough to catch fire. So it goes out once you get away from the part of the wood that was heated and dried by the flame. Do cactuses generate so much heat when they burn, that they can boil the water and still heat the next bit of cactus to 500oC? In the hot room, maybe the mass of hot air would be drying all of the cactus ready to be lit. (I suppose there must be something keeping the air in the room hot.)
But coming back to your original point, maybe a flame is hotter than air even at the same temperature? A flame glows (emits light?) but the air in a room doesn't. (Though I've never seen a room at 500oC. Perhaps that glows like a flame as well? Would air that is red or blue hot qualify as a flame, even though it isn't burning?) Air molecules however hot aren't reacting like molecules in a flame. Perhaps reacting molecules are more effective at starting fire than non-reacting molecules at the same temperature. They must be more energetic at the moment of reaction, as they then collide with surrounding molecules and spread the energy out. Perhaps if you put the reacting part of the flame to the cactus, it is a lot hotter than the flame as a whole.
