It may be that the solenoid on the starter swells when it is warm and drags enough to keep it from making contact because there is less power available from the starter button from line loss, than there is on a jump. There is a Brazilian solenoid that costs a lot less than the Japanese one. A good starter shop should know about that.
Thanks for that as well_..I will try a new battery cable first and if that does not solve the problem the solenoid will be next.
