I had this problem too. Instead of taking the thing apart, I found a suitable solution using a programmable timer:
[http://www.homedepot.com/p/Defiant-15-Amp-7-Day-Plug-In-2-Outlet-Digital-Timer-49808/203678095|Home Depot programmable timer]
Set up six events on the timer (all days) . Each event should be "on" for one and a half hours and "off" for two and a half hours. For example here's how I have it set:
Event. On. Off
1. 5am. 6:30am
2. 9am. 10:30am
3. 1pm 2:30 pm
4. 5pm. 6:30pm
5. 9pm. 10:30pm
6. 1am. 2:30am
I found that I have cold water all day long without freezing with this method. It probably saves on power too. The caveat is you can't count on having piping hot water throughout the day- only in half hour spurts six times a day. But you can at least tweak the on and off times accordingly to get hot water at the times of days you usually need it.