No such thing as a free lunch, as they say: if you want to shift data you have to provide power. It is impossible to convert all the power you provide into useful work, and the left-over power is dissipated as heat. Power dissipation in watts = (current in amperes)squared X resistance in ohms, so higher current has a big effect on power dissipation.
Current for a CF Type B card varies from 1500 mA to 3000mA, so at 3.3V power consumption = amps x volts = 5-10 W. That is a lot of power, and a lot of heat as a result, and what you are looking for is a card with low power consumption relative to its size and speed. Power consumption is substantially higher for higher capacity cards, so a 256 GB card is more likely to overheat than a 128 GB card, and is higher for reading than writing, so make sure the data is apples to apples.
The card manufacturers have not publicised power consumption data, which leads me to surmise there is not much difference.