Check out the santa fe line of dehumidifiers sold by thermastor. They are very expensive (cheapest one is ~$1000), but they are much more energy efficient than the little units that you can buy at a big box store and generally perform much better. Most of the plastic units report capacity based on a hot room having near 100% humidity. In those conditions you could fart and water would start coming out of the air. As the temp drops, it gets harder and harder to pull water out of the air, and those cheapo units just won't perform to specs. Any whole house dehumidifier (Santa Fe or otherwise) will easily outperform the little plastic units in real world conditions.
Also, a single large santa fe unit could take the place of 2, 3 or even four of the smaller units. The sante fe impact XL has an energy factor of 4.2L/kWh, which is something like 2.5 times better than is required for the energy star rating! And they can be ducted so that they can dry out a much larger area.
http://www.santa-fe-products.com/
http://www.dehumidifierexperts.com/
As for heat, well, that is a byproduct of condensing water out of the air (dehumidification). Dehumidification converts latent heat in the water vapor to sensible heat when the water vapor is condensed. If you condense a lot of vapor (which dehumidifiers are designed to do), a lot of heat will result. That said, a more efficient unit will put out less heat because it will expend less energy to dehumidify the air, and will probably run for less time.
For the record, I am not affiliated with thermacor in any way. I do own a sante fe classic though and it is just awesome. Dried out my basement in a flash.