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Comprehensive load/thermal testing was performed on a 400/400/125 MVA, ONAF-cooled transformer. It was shown that the local hot-spots in the windings, core, and structural parts rise much faster at load increase than what an exponential function based on the time constant of top oil would predict. This paper analyzes these fast rises more in detail for hot-spots in windings, core, yoke clamps, and tie plates. An alternative mathematical model of the winding hot-spot response is presented. Different cooling modes, like ONAF and OFAF, are dealt with. Also different modes of oil circulation through the windings, in horizontal (zig-zag) or axial cooling ducts, are compared. The results are verified by fiberoptic installations and tests on several large power transformers in the range of 250 - 650 MVA. Hot-spot responses predicted by the IEEE Loading Guide, Annex G, are also compared to measured values.