do u have a heat sheild on your starter slenoid? sometimes if u dont have a heat sheild the solenoid absorbs all the heat from the exhaust manifold and doesnt work, then when it cools down it works fine, the usual solution is to get a starter heat sheild

 

crews is right about the battery voltage, but i would check the alt too cuz 13.6 seems a little low usually it is 14.5 to 15 volts running. alt might be on its way out. but you need a fully charged and good battery to be acurate on the alt voltage. I really like to use amperage test myself on alternators to get a true output from it though.