Now now, MJ...
Some factors to consider [others will know more]:
[1] thermal stresses set up by unequal cooling of parts; hugely affect by boiler configuration, so you will have to be more specific
[2] ease with which fires can be pulled; solid, liquid, or gaseous fuel?
[3] in the case of water tube boilers, possibility of completely emptying the steam drum as quickly as possible to prevent its permanently assuming a banana shape
[4] loss of auxiliary power needed to continue supplying feed water during the cool-down process
[5] always keeping a sufficient reserve of suitable feed water available for this contingency
et cetera, et cetera...
CR
"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]