I searched but did not find much on this topic (other than posts that all seem to indicate why you should keep the portafilter IN the group to keep it up to temperature - i.e. so you do NOT cool the group when it is inserted.)
But, having an Elektra A3 with a quickly heating grouphead, it would seem to me that by inserting a COOL portafilter AFTER the cooling flush, you would be helping OFFSET the rising temperature of the group.
In my machine, I do notice that over the 25 seconds or so it takes my shot, the water temperature INCREASES... mostly towards the end of the shot.
Has there been any repeatable temperature tests showing hot vs. cool portafilters in an HX?