Even with what seems like a small amount of heat generated in the enclosure by the transformer, with no ventilation, and an ambient temperature not far below the operating temperature of the transformer, it will overheat pretty quick.
You can ventilate the cabinet with a cooling fan, you can even do calculations to figure out how much air the fan must move. Alternately, you could mount the transformer on the outside of the cabinet, where the heat can dissipate. However, these may be an issue in a corrosive environment or other conditions where the components must be kept sealed up.
If the cabinet must be sealed from the environment (due to presence of corrosive agents, etc.) there are cooling systems that cool the interior of the enclosure without exchanging outside air, but these are expensive and elaborate.