My 1999 Saturn sl2 will not start?

Ok i have a 1999 sl2 saturn with 150k miles on it and the battery has recently been replaced. but every time i drive it around basically until the engine gets hot then turn it off it will not start all i get is a click then once it cools down again it starts fine i have checked the battery with a volt meter it shows a strong 12.90 volts with it turned off and with it running a14.69 volts so i would figure that eliminates the alternator and the battery. any ideas?maybey the starter or the starter solenoid?