95 Camry intermittent no crank, no start issue

I have a 95 Camry automatic with 185,000 miles on it. Occasionally, but seeming to happen more often, after driving the car only a short distance, it will not start again. Ex – starts fine when I go out in the morning, but if I stop for gas on the way to work, it sometimes won’t start again. I still have power on the dash, but nothing happens when I turn the key. If I walk away for a while, or turn it several times, it will eventually start right back up like nothing was wrong. Has pretty new coils, plugs, wires and battery. This seems to happen more often when it is cold and or damp outside, but maybe that’s my mind focusing on how much it would suck to walk in such weather… I almost have to say this is a cold engine issue, because it’s only that first start and stop that it happens. I say this because I was using the car to make deliveries for a while. This would sometimes happen on the way to work if I stopped for gas, but as soon as it warmed up, I could drive it on deliveries all night; engine off and on 40 times in an 8 hour period with no issue. Any ideas?