Heat pumps are basically ACs with inverters allowing them to work at partial load (i.e. 10% pr 20% or 70%). Otherwise, they are as efficient as ACs at full load.

There are few off the shelf AC thermostats that work with most heatpumps: they are usually the on/off variety.

Remotes coming with heatpumps would do the right thing, though, and there are IR blasters that can replicate those signals and integrate into your home automation system.