Fill a five gallon bucket with the hottest water you can get from your tap. Submerge the gallon jug in the hot water.
Cold water sinks. Warm water rises. When you put the jug of cold water into the bucket of hot water, it will sink to the bottom. As it comes to the same temperature of the same water it will become neutrally buoyant.
So, just drop the sealed jug into the bucket of hot water and wait until it floats.
Shaking the jug of water every few minutes speeds the process up.
BTW: The hot water temperature at my house is set at 130ºF. (55ºC.) I don't have kids, elderly or anybody else in my house who doesn't know how to check the temperature before jumping in the bath or shower. I can keep the water temperature set where I want it.
If your water heater isn't set high enough to do the job, just use a teapot to boil some water and supplement until you get your water bath hot enough.