In the specfication to procure a power tranasformer the employer set the core temperate rise is to be 75°C but the supplier wants to supply power transfomer with 90°C temperature rise!
I think this concerns the optimal temperature of the loaded transformer inside a cabinet, before the core material begins to saturate. If the peak currents increase, or the ambient temperature increases, above that point, say, 90 degrees C, you risk a run-away situation, when the self-induction goes down and the peak current goes up, until the critical temperature when the copper wire burns through the thin insulation layers.
One aspect is the transformer core Curie temperature. The working point must be sufficiently far from this temperature. You didn't mention any transformer specifications. The powe're transformer with iron core is at 90 C degree far from Curie point contrary to switching transformer with ferrite core (you need to know exact core material specifications). Then you should checked drop of magnetic properties and losses with temperature increase. It should lead to the thermal runaway as was said at previous answer. Loss of inductance leads to magnetizing current increase. Overcurrent should activate transformer protection or it should limits the circuit operation of the switching power supply due to current limiting function. The transformer itself should be destroyed by insulation system failure due to overheating. The higher grade of insulatin wires must be used to guarantee the same life expectancy.
So if supplier produce the transformer with higher working core temperature he uses better core material and better wires. Usually is such transformer smaller with lower weight and cheaper. On the other hand it should has higher magnetizing current and higher inrush current. I recommend you to check if the magnitude of magnetizing current, total losses, inrush current and temerature safety (coordination with surrounding materials and device cooling system) meets limits of your application.