Yes, that is why I used the quotation marks & further explained that the "heat up the room" in your case would be 'a simulation of environment'.

Eg, a tree at 20°C has an extremely low chance of spontaneously combusting into a self-fueling oxidation event (lol, shit's on fire, yo) in your average environment, but those chances at 200°C are much higher.
In order to test this spontaneous combustion theory (whilst having no regard for the life of the tree) you would need to simulate that 200°C environmental conditions. ... by heating the air around the tree.
In that case you would heat up a chamber or whatever and in turn eventually maybe burn the tree.
This wound still test/prove the spontaneous combustibility thing.
You bringing open flame in contact with the tree however would not* be that - that is just actively (non-spontaneously) starting a reaction.

This is an experiment trying to test some natural conditions. Every test as such (eg if witnessed by a clueless alien observer) is you doing something actively so ofc none of it is spontaneous.

*unless the environmental conditions you were testing/simulating would be "open 1000° flames/plasma completely everywhere" ... but you may not get a grant for testing "if wood added to fire also burns"

Yes, actually. The autoignition point is the temperature at which a given material will spontaneously (as in, without a spark or the like) catch fire, given a source of oxygen.

"Spontaneous" in this usage is highly dependent on frame of reference.