There is no actual proof that dynamometer testing might damage the car in any certain way.
While performing tests, dynos dont interfere with the engines performance and more importantly, dont do any damage to it.
Some of the things that may cause damage to engines are over-revving, excessive heating, shock loading or incorrect fuel or ignition settings.
If however your engine malfunctions after performing a dynamometer test, its almost certain that the testing, if properly done, wasnt the cause of the damage.
It is more likely to damage your engine when you drive your car on the road than when you test it by the means of a dynamometer under controlled artificial conditions. You should always make sure that the dyno operator is a trained professional and that the dynamometer has an appropriate cooling system.
A 60 centimeter diameter fan is appropriate for a power run. It will prevent the vehicle from overheating.
However, you should keep in mind that dynamometer testing and setting up race cars and bikes require more controlled testing conditions. A bike or car that heats up after a few hours testing suffers from heat soak into the...