Smart Thermostat and HA


My A/C (heat and cool) is fully controllable with HA through infrared (broadlink).
Are there any smart thermostats that can integrate with HA in a way that tells the latter how to adjust temperature and fan speed of the A/C in order to maintain a certain temperature in the room?

Not looking for a solution that turns the A/C off when the target is reached and on again if the temperature deviates x degrees (this is easy to do with automations but not very energy efficient).