Coolant temp should be quite constant near 90 C. Only during DPF regen it rises near 95 C. I assume the electric fan kicked in if coolant temp was that high?

If that really was the max actual boost pressure then there is either something wrong or the remap is very mild. Those figures should come even with stock map. Usually when these are mapped the boost pressure demand is set above 3 bar (absolute pressure).

Intake air temp is measured by MAF. There is a separate boost air temp sensor on the boost hose from intercooler to throttle valve. Cooler air is always more dense so efficiency is better if boost air temp is lower. Injection quantities are slightly cut after boost air temp rises above 50 C. Especially if remapped these really gain a better intercooler like Wagner update.

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E39 530dA -02 M-Sport Messing metallic
E53 X5 3.0dA -06 Sport Stratus grey
E70 X5 40d -12 M-Sport Space grey