Be aware that many fan units use the air flow created by the fan to cool the motor. With no fan attached, the motor can heat up.
70C is not that bad for a mains motor. Overheating in a simple fan motor is usually caused by tight bearings/sleeves due to dried out or contaminated oil/grease. A more serious failure is a short in the windings due to insulation failure.
I rebuilt a fan motor recently as the Oilite sleeve bearings had dried out. The sleeve was actually packed with dried oil and dust. I soaked the oilite sleeve bearings in acetone. I have an ultrasonic bath so placed the jar containing the bearings and acetone in its water bath. A few minutes in there brought out all the old oil and muck ! I refilled the oilite bearings by placing them in a jar of hot motor oil and then drew a vacuum on the jar using a car brake system vacuum bleed unit. The bearings sat in that vacuum overnight and I could see the air coming out of the phosphor bronze
Those oilite bearings are now running very well as I caught them before they got worn due to lack of lubrication. Note that I had previously tried removal and surface lubrication on the bearings. The bearings quickly became tight again due to the dried contamination on their surface.
Fraser