When you say that they "appear after your shower...then calm down when you cool down" it sounds like it could be [a mild form of] erthyma ab igne.
The pattern of the blotches you describe [neck, torso] would be where the hot water is mainly hitting your body over a prolonged period during your shower.
It might be more obvious if you have a hot bath – you should see a definite difference, between the skin that's submerged in the hot water, which would be bright pink and the rest of you above water which would be your normal skin tone.
As the water cools down or you do after the bath then it should disappear.
If it's erythema, the only thing you can do to avoid it is not to have such hot showers or baths.
If you have an endo who is monitoring you, you could mention it to him/her and they can confirm it.
Hypothyroids are prone to it but others get it also. It can also be seen as a red/brown reticulated hyperpigmentation pattern as described below.
"Erythema ab igne (EAI, also known as hot water bottle rash, fire stains, laptop thigh, and toasted skin syndrome) is a skin condition caused by long-term exposure to heat (infrared radiation)"
It is characterized as localized areas of reticulated erythema and hyperpigmentation due to chronic and repeated exposure to infrared radiation. Patients with erythema ab igne have a history of repeated exposures to heat at a lower level than that which causes a thermal burn. Other terms used to describe erythema ab igne include toasted skin syndrome and fire stains.
Initially, the skin in erythema ab igne patients is often mildly erythematous; however, after repeated heat exposures, the classic blue, purple, or brown reticulated hyperpigmentation develops.