Can I install "2" 240v baseboard heaters in separate rooms? supplied by "1" Quad 2-pole 240 volt circuit breaker with a 10/2 or 10/3 wire?
each baseboard heater pulls about 500 to 600 watts each. Both are new installations with new wiring.
Sure.
It's normal for this sort of setup to have a separate thermostat in each room, but there's no need for a different circuit (nor for 10 Ga wire, from what you have specified so far, which could be fed by a 10 or 15A 240V breaker on 14Ga wire, with considerable room for expansion. - If they pull 600 watts each, you need to provision at 125% for a heating load as it's "continuous", so 3.125 Amps each, so 4 will fit on a 15A breaker and 14Ga wire, 6 on a 20A breaker and 12Ga wire. If 500W, 5 and 7 for the same cases.)
Nor would you need /3 wire for typical 240V baseboard, which don't use neutral - /2 wire with ground is quite adequate and typical for those - be nice and put red tape on the white wire where you connect it, though.
600 W at 240 V < 3 A, which would be fine on 14 AWG wire. But you are considering 10 AWG wire. Something is missing.
– manassehkatz-Moving 2 Codidact Oct 22 '20 at 18:31