I'm assuming you mean the sensor that plugs into the airbox? For your engine (assuming this is an UK or Aussie Corona, fuel injected, engine?), should be a MAF (mass air-flow) sensor - some sensors do measure air temperature, but on this vintage of Toyota, more like that it just measures the volume of air.
Can this cause an engine overheat? It is possible - depends on the situation. If just let unplugged - this is unlikely. If the ECM is not getting a valid air volume reading, the ECM will fall into a "safe-mode" and go off preset air/fuel/timing maps. As mentioned, anything is possible - if the ECM did not go into a fail-safe mode, it is possible that it injected too little fuel, causing the car to run lean (excessively high exhaust temps and reduced ability to control cylinder temperatures). You would definitely know when this happens, the car will not be very happy running.
Need a bit more info to help you out here. Which engine are we talking about for the Corona? When it overheated, by how much did it overheat? How quickly did you notice? How did the car run? Thing that confuses me, if the MAF sensor was pulled out of the airbox or disconnected, the car would have a very tough time running at all. Basically cannot keep an idle. Any mods to the car/engine?
If the car was running just fine with the sensor unplugged, either you have a bad termperature sensor (temperature sending unit) or bad ECM, or you have a genuine overheating problem (clogged radiator, loss of coolant, bad thermostat).