Only a slight increase in heat? As a percentage of deg Kelvin maybe.
But the globe is pretty big and heat is temperature times mass and that ain't slight - PAL.

AND considering the mass extinction of the Permmian is reckoned to have been caused by about 5 degrees shift until the Hydrates started to unlock and release methane and push the result up to 10 degrees and kill off 90% of all creatures, all of which were bigger than rabbits........... One meteor/ commet and a few volcanos that follow - should do it.

I think 0.5 deg in 10 is not slight either - as a %. It is all relative. And you won't have any relatives after that.