Yes, if there are only two wires connected to the t-stat join them and away you go. I think that t-stat is a brand called Saginomoya , you could buy something similar from a refrig parts trade supplier but I think that would be $80-$100 alone.
A simple mech type wall mount thermostat capable of switching 15 amps would work if it was hung in the return air intake to the unit, just extend the two wires and you're done. They cost us about $25, we use them to control small exhaust fans in computer rack enclosures.
If you are going to buy an old one and hear "it just needs a bit of gas" , R22 refrig, (most old units) sells out at $235 a kilo, ( thanks Julia)walk away.