Why would the puddle rapidly warm up at in the early morning? Why would it rapidly cool down in the late afternoon?
Would it not more likely warm up slowly as the sun climbed into the sky, continue increasing while the sun shone down fairly directly, and slowly cool of as the sun dropped. Which is normally warmer, 7 in the morning or 5 in the afternoon?
In applied math, experience and commom sense deserve consideration unless experiment suggests them to be wrong.