After replacing the radiator cap with a new one, there should be no coolant leaks when the engine is not overheating. If you have coolant leaks when the engine is operating normally, fix the leaks which can be in the radiator, hoses, water pump or anywhere in the coolant system. Make sure your coolant has been flushed and refilled with the proper coolant and the air bled from the system. It's assumed that you inserted the new thermostat like the old one came out and that it's not reversed in direction.
http://www.automedia.com/Keep_Your_Eye_on_the_Thermostat/ccr20041201th/1
http://www.diynetwork.com/diy/ab_auto_cooling_system/article/0,2021,DIY_13676_4098334,00.html
http://www.aa1car.com/library/2004/cm60450.htm
http://www.aa1car.com/library/overheat.htm
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