Heating elements shouldn't care, but the motors will run slower and have less torque, but still run hotter than they otherwise would for with this decreased power output.
Particularly vulnerable are things that have a high starting load like your paper shredder. Fans have decreased torque when running slower so that helps reduce the heating...unless they use their own airflow for cooling. The air mattress pump could struggle as the air mattress fills up and puts more torque on the motor.
Your heatgun gets a double whammy issue since the heater will run with the same amount of power but the fan will run slower so your heatgun will be hotter than it should and the motor will also be hotter.
Imagine an air tank constantly filled up and emptied of air. For the same mass of air being moved, you can fill and then empty the the air in smaller amounts at higher frequency, or larger amounts of water at lower frequency. But what happens if you try and move the same amount of air on a tank that is too small for the fill/empty frequency? You have to overfill it which makes the pressure inside higher than it should be and the tank is stressed, begins to burst, or leaks.
The air is the same as magnetic flux and the filling and emptying being the alternating of current. A mass of magnetic steel can only hold so much magnetic flux before it starts to "leak" which makes it inefficient and produce heat. Magnetic steel is used to make both transformers and motors.
A 60Hz transformer is smaller than a 50Hz transformer of the same power because it is designed to move smaller amounts of flux back and forth at higher frequencies so doesn't need to contain as much flux in it at any one instant to handle the same amount of power.
Similarly, two motors that provide the same power: The one that provides more of that power in speed than torque is smaller because it doesn't need to apply so much torque since that torque is spread out over more revolutions, whereas the one that is slower is larger because it has turns more slowly so more torque must be concentrated in the each revolution to produce the same amount of power. The larger motor is both mechanically beefier because it has to withstand the larger torque, but it also needs to contain more magnetic steel in the first place so can efficiently contain more flux at any instant in time which is used to produce that torque.
Trying to run either motor or transformer at a lower frequency that what is intended but trying to draw the same amount of power from it as before makes the magnetic steel "burst at the seams" so to speak. That's why your laptop and computer power supplies run at kHz or MHz. So they can use a tiny transformer and inductors for the same power.
So back to your original question, it is not that the 60Hz runs cooler than one built for 50Hz. They both run at more or less the same temperature as each other because that's how they are designed. But the one built for 50Hz has more steel in it to account for the higher flux concentrations present. The 60Hz is built with less steel because it doesn't need as much steel. So I would expect a 50Hz transformer to run cooler than it normally would at 60Hz (though being oversized introduces other types of losses, as well as cost).