Looking for a timer 20 mins on 5 mins off
Does it matter if the hose has time to heat up? 

Isn't the sun imparting the same amount of radiant energy to the water through the hose regardless of the temperature of the hose?  Therefore you can just circulate continuously.  If you're trying to get the output temperature to be a particular value you can restrict the flow with a gate valve  on the pump output so that the time in the hose is longer

For conducted heating the rate of heat transfer is related to the difference in temperatures, but the amount of energy input is the same.