The difference in temp I experience is a lot more that a couple of degrees but I would be interested in your findings nonetheless. My machine is next to the kitchen sink and I rinse the handle after each shot so, even when using hot water, the portafilter cools down considerably and needs to be brought back up to temp. If I don’t, then consistency falls off a cliff.
Just to be double clear on this; I’m not claiming to have any scientific insight into what is going on nor am I arguing causation when all I can observe is correlation. I am sharing my observations with an interest in finding out more and hopefully helping others.