Where is it leaking? If you had a bad thermostat, it would either not open (which wouldn't let coolant flow from radiator to engine) or wouldn't close. It would not leak from there. If you are losing coolant you need to find out from which hose or radiator or gasket it is comeing from. If you are losing coolant and it is not leaking onto the ground you might have a blown head gasket or (eek) a cracked head.
I would first check for hose leaks (e.g. Loose ends, small holes in the radiator hose) Next I would look to see if there is maybe a pinhole leak in the radiator. This is easilty fixable with a "radiotor sealant" ("metal ions") that you can just pour in the radiaor, you can pick that up from any autoparts store. Just find where the water is leaking from. Hopefully its not as he said, cracked heads.