We investigate the high-frequency Hall effect on a two-dimensional triangular lattice with nearest-neighbor hopping and a local Hubbard interaction. The complete temperature and doping dependencies of the high-frequency Hall coefficient RH are evaluated analytically and numerically for small, intermediate, and strong interactions using various approximation schemes. We find that RH follows the semiclassical 1/qn∗ law near T=0 but exhibits a striking T-linear behavior with an interaction- and doping-dependent slope at high temperature. We compare our results with previous theories as well as Hall measurements performed in cobaltates.