thermostat

The thermostat works by staying closed when the engine is cold, blocking off the radiator, to allow the engine to warm up quicker. Once the coolant gets hot, the thermostat opens up and allows coolant to flow through the radiator. With no thermostat, the engine will take forever to get up to normal operating temperature.

Your car will run without a thermostat, but it won't run properly. It's a bit unlikely that anyone would simply take the thermostat out and leave it. What is very likely though is that there is air trapped in the cooling system from not being refilled and bled properly. There is a bleeder valve by the thermostat that can be used to relieve trapped air. Even with that it can be a bit tricky to get it all out, but until you do it will not cool or heat properly. I've heard that filling/bleeding the system with the car parked facing uphill helps, but I haven't actually tried it.