1993 Toyota Corolla removing the thermostat

You would have a lot more to worry about other than fuel consumption if you were to remove and leave the thermostat out. Leaving the thermostat out entirely reduces the pressure that your cooling system operates at. This decreases the temperature at which the coolant boils and can cause bubbles of air in the coolant at the hottest places in the engine. These bubbles then act as a thermal insulator which makes those hot parts of the engine even hotter. But your temperature guage will still be showing 'normal' temperatures. If the engine runs hot in one particular area, it can damage the piston rings eventually causing the car to smoke, burn oil, and eventually cause total engine failure.

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In addition to what bluelightnin6 said:

It will prevent the ECM from going into closed loop, where O2 sensor feedback controls engine. This will increase fuel consumption, cause the engine to run rich and eventually ruin the convertor.

If you are having a overheating problem, removing the thermostat, is only a band-aid. Have the cooling system pressure tested and get the problem fixed.