Has the human capacity to heal from burns evolved due to actual burns throughout human history?

I just burned myself while cooking, and it occurs to me that although this has happened countless times, my skin always heals itself rather well after burns.

In this post I make various assumptions/guesses on topics I know very little about, so please forgive me of my uninformedness. I am just trying to explain the premise of my curiosity.

This got me curious, and it appears to me that it takes about 1 million years for lasting evolutionary change to take place.

Is the current ability of humans to heal after burns a result of humans being burnt throughout the hundres of millennia? Or perhaps the body just has a general healing response, and it kicks in for burns in the same way it does for any other injuries?

It occurred to me that there are rather few circumstances in nature that would produce temperatures hot enough to produce burns in humans. I realise volcanoes, hot springs and fires caused by lightning are notable cases, but it appears to me that these phenomena are rare enough that humans would seldom come into contact with them (especially because humans would probably avoid them).

This leads me to the assumption that the majority of humanity would only start getting burns relatively frequently after humans started controlling and using fire themselves. I have read up on the subject, and it does seem that humans have been using fire for at least hundreds of thousands of years, and possibly for up to one million years, according to some research.

However, would this have been widespread enough, and for a long enough time, for the current response (healing of burns) to evolve? Or is the healing process just generalised for all injuries?