Transformer Inefficiency and Heat
Transformers are not rated by "efficiency", they are rated by losses, although the efficiency at maximum load can be defined. So you cannot assume that at 250W of load the transformer will dissipate 10W if at max load (500W) it dissipates 20W, it will dissipate more than 10W. This is because transformers have two types of losses, "load losses", and "no-load losses". Even at zero load a transformer will run warm.

Load losses depend on wire resistance of coils, and are proportional to load.

No-load losses are independent of load, they occur due to continuous magnetizing and de-magnetizing of transformer core, with two basic mechanisms - hysteresis losses, and eddy losses. These losses depend on quality of core construction and materials. To reduce eddy losses, the cores are made of thin sheets, so the eddies can't spread over much of core volume. Hysteresis losses depend of magnetic alloy composition. Some portion of magnetic field escapes the core and induces eddy currents and warm up surrounding conductors (mounting hardware, bolts and brackets), which also adds to no-load losses. Without knowing precise details of core construction and manufacturer's data, you can't "compute" these losses. For example, cheap knock-off transformers for Christmas decorations can stay pretty warm even when the lights are off.

ADDITION: I happen to have an old 200 VA auto-transformer 115:230V, model SU-38, made by TODD SYSTEMS. In idle (no load) mode, with ambient of ~25C and sitting on a pack of papers, its core gets to ~40C, see the thermal image.: