Ability to transfer heat away from the area is also a factor, since core temperatures are only estimated along with standard heatsinking practises to give ratings.
The rating you are using should be based upon continuous duty if that is the duty cycle you expect can occur.
Heat causes two serious runaway effects: increase in impedance (generating more heat), and breakdown of insulating materials or flexing of coils and breakage or shorting. It is important to operate the transformer in ranges appropriate for the cooling capabilities and environmental temperature expected.
Both types of failures should be considered for safety:
(1) open circuit failure, with accompanying changes in loads/voltages on other components,
(2) short circuit failures, both across primary and between coils. Each could have its own consequences.