The only physical connection the tranny has with the cooling system is via the ATF/coolant heat exchanger.

But usually with tranny work you pull the oil lines going to the heat exchanger if needed, leaving the cooling system untouched and intact.

If they pulled the heat exchanger from the distribution plate that would spill the coolant and necesitate a refill and bleeding of the system.

If the bleeding after refill was done improperly it would result in low coolant messages.

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04 X5 3.0i auto
03 X5 4.6is