Why does my 2004 Dodge truck sometimes start and other times won't even turn over?

My truck wouldn't turn over, click or anything.  I checked the battery and connections
to starter, no problems.  When the tow truck came and I had to put it in neutral at the
gear shift and at the transfer case, I tried one more time to get it started and it started
right up.  I drove it all the next day and no problem, although my air temperature
reading in my cab overhead said it was 124 degrees outside.  It's January in Michigan
and that's not even close.  Now today again it won't start or click or anything.  Any
ideas?