How do you simulate the warm water?

Oh, lol, now I get your question. Yea, it turns out the silence and lack of distractions are what produce "shower thoughts", more so than the act of showering itself.

Doing any relatively rote act like washing dishes, walking places, etc can also give rise to them. Not having a device in your hand to constantly steal your attention really helps though.

Showers are generally considered to be relaxing separately from the “shower thoughts” phenomenon.

Couldn’t the relaxation be a factor in generating shower thoughts?

I suspect that essentially none of our non-ancestors were predated in a hot spring, unlike walking etc, so there may be an environmental cue driven induced relaxation that doesn’t exist for many other activities.

Yea, you relax, and then your brain produces random thoughts about things.

I suspect it's just about getting the space to relax, which is why I frequently have thoughts when staring at the wall, or taking a walk, or washing dishes, or doing any other myriad activities which are relatively easy on brain processing.

Solitude is extremely powerful.

I find pacing to be helpful. As long as there’s not a lot of poles to walk into accidentally. So while outside walks can be more focused you do get the odd head bang.

Play it on a speaker.

With a faucet my good friend!