Agree with Fixer: the reason that it crashes when the fan goes with full power is = the reason that the fan goes with full power is heat = the fan tries to get rid of the heat. Fans don't cause heat, they get rid of it.
Good old housewife method: vacuum cleaner. Or pressurized air in an aerosol can. One solution could be a laptop cooler you place under the laptop. And, fans can be cleaned with a moist tissue, perhaps some light solvent --- BUT don't do this with computer turned on!!! If your fans are dirty, their effect drops, drastically.
You need both hot air flowing out and cool air flowing in. Check the ventilation, in and out may be covered with dust?