What is controlling this baseboard heater without a thermostat?

It may be a vestige of a larger whole house baseboard heating system, where there was a central t-stat somewhere and all of the baseboard heaters were controlled from that one point. If that system was replaced with a central forced air heating system at some point and just this one room still has the baseboard heater (i.e. because there was no duct run to it), that baseboard may still be connected to a central t-stat somewhere that is buried or hidden. So it gets satisfied by your central heating system and shuts off, killing your sole remaining baseboard. The reason I know this is that I had that exact situation in a house in Seattle, where baseboard heating was the norm back when electricity was almost free. I put in central forced air gas heating, but had no ducts going to a seldom used basement room, so I left the baseboard there to be used only when the room was used. I didn't realize that the t-stat in the wall in the basement stairwell, which I thought was abandoned, was still active and controlling that baseboard heater.

This is not a thermostat problem. If the baseboard unit is not getting hot, then either it's designed to run at a low temperature or the electric line feeding it has a limiter somewhere. A thermostat merely makes or breaks the connection to the heater until the room temperature reaches the setpoint.