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What is model on the outdoor unit and how sophisticated a thermostat do you want?
His fan coil can be used with an air conditioner or heat pump is hy I ask about outdoor unit.
As for sophisticated, thermostats will run from 30 bucks for a basic thermostat to a couple hundred for programmable or wifi capable. We will go from here.
OK I see now you already said it is a heat pump
Do you want a basic manual thermostat or programmable?
Ok, there are many that are compatible. All you need to do is make sure it says 2 stage heat/1 stage cool.
My choice would be the Honeywell RTHL3550. You can purchase at Lowes for about50 bucks. Very reliable and accurate thermostat.
I recommend taking a picture of old wiring before removing thermostat.
Then I will be happy to guide you in hooking up and setting up the new thermostat to match your system