50Hz equipment on 60Hz supply will usually operate with very few problems.
It is 60Hz equipment on 50Hz supplies that has problems of overheating primarily due to issues with the magnetic circuit.
Operating 60Hz transformers at 50Hz will cause the core to saturate, at which point the impedance drops to nil and the coil is essentially a short circuit. The transformer must thus be voltage derated by 20%. I had the misfortune of witnessing this first hand when some 60Hz transformers were mistakenly installed at a 50Hz site- the engineer that designed it swore up and down it would instantly explode into flames, but thankfully his calculations were just conservative enough to run. We recorded twice as much kVA going in as coming out, and even at light load with covers off and big fans blowing, the transformers were close to the max rated temperature.
Operating a 50Hz transformer at 60Hz will often cause excessive core hystersis and core heating due to the larger core and especially due to the wider core laminations, which provide much lower impedance to eddy currrents. I have not witnessed it, but another engineer I work with witnessed an oil transformer explode due to heat generated form this.
Dual-rated 50/60Hz transformers use thin 60Hz core laminations built up to a core size thick enough to support 50Hz at the rated voltage without saturation. They're generally less efficient than dedicated 50Hz or 60Hz, but are often cheaper as a single design and assembly line can provide equipmenet that works anywhere in the world.