I am looking for any substance that would be unstable or dangerous when it is cooler or not on heat, and is stable when it is being boiled
Well, in theory, a few compounds could become explosive when crystallizing out of a solution (which is promoted by low temperatures) though I do not think that "turning off burners" would be enough. The "best" candidate I can imagine would be "azidoazide azide" which can detonate for... just any reason! But nobody uses it, just because of that.