If your brew water is, say 93°C, through the process of kinetics, advection, dissolution, diffusion, and a whole bunch of other physics shit that'll make your eyes go dizzy, the temperature of the espresso emerging from the bottom of the basket will lose around 7°C, so you'd have espresso at 87°C before it hits the spouts. Those spouts, if left in the group head, will be under the brew water temperature, but not by much - it very much depends on the ambient temperature. But the spout is below the basket and group head, so you'll lose a little more heat too, so you could argue that perhaps the spouts are around 90°C - but I'd argue that'd be at most. Here again the process of cooling begins again - the initial espresso will cool down the spout, and the cooling will only continue as more espresso moves down the spout.
The bottom of the portafilter wouldn't reheat the espresso, the espresso would cool down the spout. But if you start with a cold spout, then the espresso would cool down - and I think that's the effect Berg got, where the floral aspects of his espresso became more apparent.