@mx_tifosi: I've no idea how much steam/water is needed, it all depends on the type of steam engine you want to run: turbine, piston? How many stages?
@enkidu: Unlikely this will let go, you just need a blowoff valve aimed away from the cockpit, and it'll just go puff like overfilled oil at the start. Is it even possible to do radiatorless cars? In this case fuel and water are topped off every pitstop, and the cars keep cool by boiling water and venting off steam, like NASA spacesuits. This assuming that the steam engine takes a lot of energy off the steam circuit, of course.
Regarding the brakes, I'm sure if liquid cooling is allowed (currently banned) the teams will jump at the opportunity to recover heat from the brakes. This removes the need for brake ducting, and the coolant can be routed through the wishbones, improving aero.
I could not think of any other solution apart from steam
You could also attach a generator to a
Stirling engine
Or
go straight from heat to electric power.
I read the other day a bunch of Aussie highschoolers made a coolantless aircon, using the Peltier effect. So yah, it follows that the reverse should be doable. And if it's only marginally doable, where else to test it but F1?
PS: I'm sure some of you think I forgot to take my medicine for suggesting a radiatorless engine. At least
one guy is trying it out, though. But not with a closed-circuit steam engine.