It is very interesting that this question was asked today.
I just replaced a 14-year old 11-gallon Isotherm
waterheater that was doing exactly the same thing the OP described.
The tank would sit quietly for hours with the AC power to it turned off and no other heat source applied to the tank. Suddenly the Shurflo 3.8 GPM freshwater pump would take off and start running and the overpressure valve on the tank would open and close very rapidly while discharging luke warm water.
Sometimes the pump would stop running and the valve would stay closed. Other times the only way to stop the over pressure valve from flowing water to the bilge
was to shut off the Shurflo pump.
A few seconds after shutting off the Shurflo I would turn it back on and the overpressure valve would stay closed.
I lowered the pressure on the Shurflo and the problem continued. The hot water and cold water coming from the galley
sink, closest to the Shurflo, showed no unusual pressure or pressure fluctuations.
Opening the galley
hot water tap sometimes will cause the over pressure valve to close and stay closed, other times nothing will cause the over pressure valve to stop cycling open and closed, except for shutting off the Shurflo.
I installed a NEW 11-gallon SPA 40 Isotherm
water heater earlier this week. Three times in the last two days the same problem occurred with the new heater: with no power or heat to the water heater - the overpressure valve starts surging open and closed and I have to turn off the Shurflo to stop the discharge.
Each time the over pressure valve starting cycling open/closed I checked the water temp coming from the hot water tap and found it to be only slightly warm.
It has now been 12-hours since the last time the over pressure valve opened.
I do have a filter in the freshwater line to the Shurflo and am pretty sure there is nothing but really clean city water is being pumped into the Isotherm.
SO - I have the same question as the OP!