Has there been a discussion about this?

It seems to me that a short pre-infusion would equate with a higher initial and average brew temperature.

I think this is one reason that a gusher shot on a lever group is so bitter.

Have there been comments on the pages and pages of recent lever temperature and thermosiphon discussions that have discussed this? If so I don't need to rehash.

Flint, you are 100% correct in your assumption that a shorter preinfusion will result in a hotter shot then a shot with a longer preinfusion.

In my Lambro, the beginning shot temperature will be reduced by 0.5*F for every 7 seconds of preinfusion. I do a long 15 second preinfusion, but mainly due to the lower boiler pressure I set (0.62 - 0.8 Bar). If I increased the boiler pressure and did shorter, more usual 7 - 10 second preinfusion, the shot temperature would be hotter then if I did a longer preinfusion with that boiler pressure.

Here is more on the same topic: Faema Lambro Brew Temperature

The group will continue to sink heat until it reaches equillibrium with the water. The larger the group the longer this will take (probably not relevant for commercial groups, since the water would eventually get TOO cold).

With my Sama I like to wait a few seconds at least to let the group cool the water. How long I wait depends on how warm the group is. Since I do multiple pulls, this is quite important.

I've never bothered to measure group temperature, but just do it by feel. But it should be pretty easy to develop more precise routines with commonly available temperature meters.

PC