Those temperature limits are set by the tests that were done for certification, from subsystems exposed to ultra-cold and ultra-hot chambers, to the entire aircraft exposed to the ambient temperature and "cold-soaked" for many hours.
Generally, the high temp is set by the ability of the systems to cool themselves, especially the hydraulics and engine compartment components and sometimes (rarely) electrical components. High temps are typically derived by projecting the temperature in the closed compartments as they soak up to max temp (typically a zero wind hover). The engine compartment is often where the hottest places are.
For cold, the worst items are almost always the hydraulic servos, which shring so that larger gaps allow big leaks until the fluid and the cylinders warm up.
When you hover with a downwind and reingest your exhaust, the local heating can be pretty fierce, some helos have problems where the exhaust impinges on the fuselage, and literally burns the paint or over heats the composite structures. Avoid those downwind hovers, by all means. You could be overheating any components that rely on cooling air. Engine compartments on many turbine helos are cooled by having an ejector effect, where the exhaust pulls compartment air along with it, thus ventilating the compartment. If you hover for prolonged periods in a downwind, you can force the ejector to have nil effect, or even entrain exhaust into the engine compartment, with dire results, even fires!
Generally, the low and high temp limits are real, and damage or even unsafe conditions can occur due to abuse.