I have had. Polycythemia vera for 19 years. I am 82 this year.
Lukewarm showers! As cool as you can stand. Many people with PV opt for washing at the sink over showers because such a wash does not heat the body nearly as much as a shower or bath.
Hot water raises the body temperature, and that in turn causes tiny capillaries to rise to skin level in an attempt to cool your blood/body. Well, sludgy blood due to PV has a hard time moving though those tiny capillaries. Sludgy blood sticks to the sides of the capillary walls. The body, in turn, reacts by sending histamine out to those capillaries. Well, histamine causes itching. End result: Hot showers and baths make us itch.
So, many of us either take brief lukewarm/cool showers or wash at the sink in lieu of bathing. Some even use wet wipes (like the ones they provide in hospital; you wipe your skin with them but need not rinse off afterwards).
Thank you for this easy-to-understand explanation!