Are temperature rise and actual surface temperate related?
Yes, the more heat a transformer generates, typically through increased load and/or harmonic distortion, the higher the temperature rise. The more the internal temperature of the transformer increases, the hotter the surface temperature of the windings and core.
The important thing to note is that while related, temperature rise and surface temperature are not the same, surface temperature will always be cooler, often significantly cooler, than the "Hot Spot" in a transformer. This hot spot dictates the unit's temperature rise and represents that area of greatest stress to the insulation system. Temperature rise is typically measured by sensors mounted internally in the coils where the manufacturer believes the hottest temperatures will occur and cannot be measured by surface temperature.