The thermostat controls the temperature of the engine coolant, if it were stuck closed you'd risk overheating, open and the engine would take a long time to warm up. Regardless the coolant to the heater core should be the same temp as that in the engine. You stated the heater hoses are cold but engine is warm. Have you felt the radiator hoses to confirm this or assuming it? If the engine is indeed warm I don't think the engine thermostat is going to have a bearing on your problem, the heater hoses should be on the engine side of the thermostat.
Have you ever had heat from the machine or did you inherit an existing problem?
It sounds like there's a blockage somewhere. Have you verified that the actuator valve is getting power from the switch? Is it grounded properly? Any kinks in the hoses that would prevent flow? I had an instance once where the fitting on the block that the heater hose connected to clogged with debris on an old truck. Your going to have to start tracing the flow and verify it has a clear path.