Apologies, first, if this answer is not up to the usual high standard. It's hard to concentrate after a week of four hours' sleep a night. And it takes only a couple of degrees: anything much above 18C and half of will us will spend the night tossing and turning.
So how to maximise your chances of a good night's kip in such conditions? The following are culled from a variety of sources - some expert, some I suspect not. But somebody swears by each and every one of them.
Try to cool your bedroom down: keep windows and blinds shut during the day, then throw them open at night. Get what air there is circulating. If it's still baking, consider decamping: is there a cooler room in the house? Heat rises, so if you you sleep upstairs or in what used to be the attic, chances are there is.
Air conditioning is expensive and bad for the planet but, if you can stand the noise, a decent fan can help. Some people place ingenious home-cooling devices - trays of ice cubes balanced on stools, wet towels suspended from chairs - between fan and bed, so the air that reaches them is ready-chilled. (Others, I'm told, peg their top sheet to a fan at the bottom of the bed, delivering a non-stop flow of air exactly where it's needed.)
Next, cool yourself down. Avoid activity before bed, or stimulating drinks. Take a cold shower. Alternatively, chill just your hands, feet and head. My friend Alison says (seriously) a pair of wrung-out wet socks works a treat, as do soggy bandanas or wristbands. The Egyptians swear by a damp top sheet; I once met a Texan in Corsica who sprayed and then froze (I'm not kidding) his sheet and pillowcase every morning.
Try them, do. And if you find anything better, let me know.