How inaccurate is safe, and is there much/any risk of thermal shock issues causing patterns if you're going too wide in temperature difference?
As far as this issue is concerned, there are basically two types of film out there: film which has been properly prehardened by the manufacturer, and film which hasn't. If the film has been made in the last few decades by Kodak, Fuji or Ilford, then film will withstand pretty much any thermal abuse you throw at it. I switched from 50°C hot water to 15°C cold tap water between two consecutive tank fillings, and had no problems whatsoever. As it just so happens, the vast majority of color films are made by the big three, Agfa Precisa is a Fuji product AFAIK. Not sure about Rollei or Lomo products.
The main reason I stated 'last tank filling before next photographic bath should have correct temperature' is not film stability or anything, but that an incorrectly tempered tank will shift the temperature of the next bath, and not necessarily in an accurately predictable manner.