redleader:
Your calculations are correct (although my teachers at school would cry if they saw your abuse of the units ;-) )
beaverpants:
Using the numbers redleader provides tell you that the temp of the water in the tank will increase with around one degree C per hour. 8h gives 8 degrees.
What you really need to think about is how much water the household uses per day. When you say 30min between "the water flows" what do you meen?
Do you change all, 50 gal, of water every 30 min or do you flush the toilet every 30 min which introduces only a little new water to the system.
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