Yeah, first shut down, then open case, then run to test fan, then switch off and carry on. Making sure all the fans can spin freely (by twirling them with my finger while off) would be the first thing I'd do. The second would be to vacuum up the dust inside.

And while you really can't get electrocuted from the innards of a PC, the interior of the power supply box itself is wicked dangerous, so don't stick any screwdrivers or suchlike inside that box's vents, even with the power off.

Knowing Cleo, this is not an issue. I'm more afraid that she'll be too timid to do anything herself and pay a lot of money for something that could be done at home with a dust buster, than that she'll do something dumb.