Whether there is visual degradation of the print or not due to poor temperature control between processing baths, why compromise and risk it?
It is SO easy to get all processing liquids to exactly the same temperature by using a water bath. Give the liquids time to stabilize.
There is absolutely no reason not to exercise precision in the darkroom.
I personally believe that the harder one tries to eliminate large variations in the process, the better off we are, not only with respect to graininess, but also to achieving our expected outcomes with as little material waste as possible.
All errors are cumulative, and if we skip precision at every stage we end up with a process with pretty wild variations and poor consistency in our output. Yet with black and white darkroom chemistry it is stupidly easy to achieve. All you need is a thermometer and a little bit of patience.