First of all, to a Chemist, Oxidation covers a huge area and it does NOT always genereate heat and light. In fact, most oxidations (like rusting) do not. (Well, actually, most do generate heat, but some so small we don't notice). And for all those reactions, there really is no practical lower limit in temperature (above absolute zero, that is) that will stop it. The reaction rate, though depends on the temperature, so that it is much slower when colder - just does not stop altogether.
Now, the specific classes of oxidations that we call flames are just those that proceed so rapidly and emit so much energy in a broad range that some of it is in the heat frequencies (infrared) and some in the visible light fequencies. In virtually all such situations, if there is enough energy output in the visible light region for us to see a flame, there us bound to be much more energy output in the adjacent lower-frequency range known as infrared - HEAT! So if you see a flame, you are virtually guaranteed a lot of heat. That is because the rapid free-radical reactions in these systems produce huge numbers of atoms and molecules at high and unstable energy states - and many such states - which release that excess energy by radiating it out at many frequencies (because there are so many energy states in total). The higher energy emissions are what we see as visible light. But that usually leaves a molecule at a lower but still unstable energy state, and it emits more energy again, only this time at lower frequency in the infrared region. So, bottom line, anything we can see a flame on is going to produce enough heat we would call the flame "hot", certainly to our skin!
So, is there is minimum temperature below which combustion can occur? No. Hypothetically, for some particular systems the combusion might begin and then stop. You see, combustion is a chain reaction - to keep going it needs some of the energy being emitted by the burning molecules to get the next ones going. And if you can remove that emitted energy (much of it in the form of excited free radicals) very fast, you might stop it. That is exactly how fires are put out with water. The water added absorbs huge amounts of heat energy and traps free radicals without producing any replacement free radicals to keep the chain going, and the reaction is stopped. But for most practical systems just having the initial flame in a cold chamber won't do that. The cold chamber is a place for infrared emitted energy to flow, but that still does not stop the free radicals that are the key propogators of the chain reactions.