Is it wise to install a heat pump type system to cool and heat your house in a climate like Houston, TX? High humidity, high temperatures 98+ degs, does not cool down at night, maybe 82 or 85 degs low. I know heating is not an issue but can a heat pump handle bringing the temperature down from 98 degs to 80 degs inside? I am not unreasonable and know even a good ac unit has a hard time keeping up with a 20 deg differential. Any advice would be appreciated.

A heat pump system is exactly like a A/C system except the heat pump has a reversing valve. If you are looking for the cheapest form of heating to help cut your utility bills and heat pump is the answer for most people.