A sticking thermostat can cause your car to overheat and will not show up as a leak. This problem can be hard to detect but here is an easy way to check. Feel the radiator hoses when the car is running and if the top hose is cool or cold this means that the coolant is not circulating through the cooling system which means you could have a stuck thermostat. Normally the upper hose will be hot since the coolant is exiting the motor and getting ready to go through the radiator. The lower hose will always be cooler since the coolant has just gone through the radiator. So normal would be engine running at operating temperature and the upper hose is hot and the lower hose is cooler.
If you think that your thermostat is bad here is a way to test it. First you will need to remove the thermostat from the engine. On your stove boil water and put the thermostat into the boiling water. The thermostat should open when it reaches a temperature between 180 degrees and 220 degrees. If it does not open you will need to replace it. You will want to replace the thermostat with the same on that came with the car. If you look on the thermostat you will see a temperature rating stamped on the outside. It is always best to use OEM parts when available. You also do not want to change the temperature range of your thermostat. By changing the temperature rating you are asking for trouble.