Hrm... I've never heard of water suddenly changing temperature. I mean, unless you put the hedgie under the water before it's had time to heat up.
Either way, the water in my complex will never get hot enough to scald a hedgie. I know this because when I lived in New York, I could turn the hot tap water on and make tea directly from the faucet. When I moved to Texas, I couldn't. Nor could I generate a steam bath in the bathroom. So I asked the complex managers about it, thinking I had a serious problem with my water heater and they told me they put temperature controllers on the water heaters so that kids couldn't accidentally burn themselves. They keep them standard at about 120 degrees F, which becomes significantly lower once it gets to my tap.
But, in the event that this device breaks or something, I can see how being cautious would be in Jack's best interests. I am hesitant to change this pattern though, because running the water before Jack goes in is a cue to him that it will be bathtime soon and he needs to stop what he's doing, grab a quick snack or whatever because he's getting picked up soon. With his eye and all, I don't want to break routine with him. And the sound of the bath is familiar to him. Like, he knows the difference between running the bath water and brushing our teeth running water. Any suggestions on how to keep the routine, but also keep him safe? Maybe make a Hedgie Bath Butt Barrier!!