Cooling fan spins extremely fast, noisy on startup
Now that you have done some measurements, you could make some conclusions.


  The voltage over the fan is reported to be constant, but the current
  starts at 110-115 mA and reduces to 90 mA over time.


With limited knowledge of electronics you can conclude that the resistance of the fan is not constant as the resistance determines the amount of current through the fan. So the fan resistance increases over time. This could just be a manufacturing problem or characteristics of the fan. You could try to replace the fan with another fan to see if this fixes your problem.