If you don't hear it after it sits overnight, no matter what outside temp is, then it needs to be replaced. It should stay on for quite a while when you first start driving after a overnight startup. Mine would go off in a block or so and I suspected it was getting weak, so I replaced it. Now it will stay on for a half mile or more, if you keep rpm's down under 1500 it stays on longer. If you get it over 1500 rpm's or more it will unlock faster.
Mine will lock up on 90 degree or better days with a/c running, and driving at highway speeds (2000 rpm's or better), when you get off an exit and come to a stop an idle for a bit it will come on when you start bring the rpm's up and usually by 1500-2000 rpm it't will unlock, again if you keep it below 1500 it will stay on longer.
I never have any overheating problems. I installed a real gauge this fall so this summer I will be able to see were its at, but so far even at 55 degrees with winter front on I have not seen more that 200 degrees.