Does removing the thermostat affects the performacce of the car?

Removing the thermostat will most definitely affect the performance of a car. If it's old enough to still have a carb, the engine will always be on the lean side, since the air is more dense, plus the lower temp doesn't atomize the fuel as well. If computer controlled, the ECM sees this as an abnormal condition, and either goes in the limp-home mode, or never allows the engine full power by restricting ignition timing and transmission shifts.