I was leaning towards the leaky hot water pipe / faucet idea first - since it's the most logical [per Mr. Spock! He is a Plumber, 'ya know
].
This is usually coupled with an almost coincidental increase in water consumption!
I headed this way due to many, many Tshoot Q's and trips concerning high KWH consumption and resulting water consumption!
If the leaky bugs are not to blame [AKA no leaks], then try "Step 2", which is to verify the T Stat is operating properly and that no one has set it to "Boil" [AKA the highest setting].
Cannibals may prefer the "Boil" setting
<joke>
If still a head scratcher, make sure the culprite for the increased KWH usage is indeed the water heater [so you don't tear it apart and your friend walks in and says "Oh, I forgot to mention the outside lights that stay on 24/7!"].
If all signs point to the water heater, check the elements for leaks [electrical leaks] and the correct wattage.
If all these points fail to turn up a culprite, hire an Excorsist!
Scott S.E.T.