Depending on the age of the house, the valves could be pressure balance valves. These are supposed to adjust the output to keep the hot and cold in balance if the pressure drops (like if someone flushes the toilet). Any clue if the dishwasher, washing machine, or some other device is turning on when this happens?
The pressure balance valves sometimes get sticky and can't adjust. If the house is old, then you may not have this type of valve so you may want to replace those with the newer, required (upon new construction or remodel) valve type. I consider a thermostaically controlled valve an upgrade. I like mine. I leave the temperature adjuster the same, winter or summer, as the WH is full, or nearing empty, it keeps the temperature the same until there just isn't enough hot left in the tank.
If you have pressure balanced valves, you might be able to remove, clean, and lubricate the spool valve that is the heart of the pressure balance mechanism.
Could be something I haven't thought of...see what others have to say.
