Can I use 14/3 wire and a 20 amp double pole breaker for a 240 volt baseboard heater?
Only if the heater draws less than 12 amps would 14 AWG be adequate.  And that would require a 15 amp breaker, not 20, to properly protect 14 gauge wire.

Space heating devices require wiring to be 80% derated which is assumed by the electrical code to be "on" 100% of the time.

A heater rated up to 24 amps requires 10 AWG and a 30 amp breaker.

A heater rated up to 16 amps needs at least 12 AWG and a 20 amp breaker

A heater up to 12 amps needs at least 14 AWG and a 15 amp breaker.

The heater will have volts, amps, and watts on its "ratings plate".