Since you didn't notice the fan clutch engaging, that should be your first course of action.
I worked in an auto parts store for years and I need to add one recommendation:
If you replace the fan clutch, get an OEM unit rather than any aftermarket one. We had more problems/returns for fan clutches than any other single kind of part. One GOOD customer with a motorhome was overheating and he figured the fan clutch was the problem. He put one of ours on, the problem remained. He put another on, same thing. We got one for him from our competitors across town (different aftermarket brand) and it still didn't stop the overheating.
He bought a GM fan clutch from the dealer and the overheating problem was gone.
Phil