6S will run cooler because the motor will draw less CURRENT at the higher voltage, assuming the motor is the correct KV as said earlier. A 6s 3000 mah 1400 KV setup will run cooler and just as long because the CURRENT draw is less and the motor is more efficient at the lower KV than a 2200 KV setup running 4S.

A high C rated battery is not as critical with the higher voltage because the CURRENT draw is lower.

Both batterieswill do the same amount of work assuming everything is equal, 6x 3000 =1800 - 4x 4500 = 1800.

Higher voltage is more efficent at doing the work because it will draw less CURRENT and created less heat.