I have equipment in several L(3) DCs. I'd say that is generally the exception however I have two notable facilities (smaller type 3) that have troubles on occasion... reaching into the 80s as you commented. (Usually during the warm southern summer days) .
I found that my getting to know the facility manager/personnel very useful. They gave staight up answers and have done what they could to assist.
I'm a few years removed from having direct involvement in our DCs now, so I
don't have an example on hand to look at. Is cooling (and in-cabinet
temperature) not a part of the SLA? If it is, then there shouldn't be a
question of the DC staff brushing off complaints about the
temperature–either L3 should fix it or pay the penalties. If it isn't,
then I'd suggest having a look at your contract (and possibly looking a new
DCs) at renewal time.