I am assuming you have the M103-series engine...
You say no water in oil...does your coolant tank have oil in it?
If so, you probably have a head gasket that has breached.
When sitting, do your auxiliary fans come on at all when the temps begin to climb? Disconnect the coolant temp sensor and see if the fans come on immediately.
Just giving you some things to look for...
The cheap components would be the aux fan switch and the coolant temp sensor...but throwing parts at the problem is not the solution.
2009 ML350 (84K) - Family vehicle
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2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car