We report on thermal phase curve measurements of Saturn's main rings by the CIRS infrared spectrometer on-board the CASSINI spacecraft. The extensive data set acquired by Cassini since its insertion in orbit around Saturn provides for the first time spatially resolved temperature measurements over broad phase angle ranges and for different solar elevations. Each of these curves exhibit a nonlinear variation in temperature with phase angle, with pronounced surges at medium to low phase angles that we interpret as an opposition effect in thermal infrared. The transition from a relatively flat linear regime to an exponential behavior in the A and B rings occurs at phase angles of 30° to 40° and is significantly broader in the C ring and Cassini Division. Analytical description of the phase curves is provided to serve as basis for future modeling work. The role played by mutual shadowing as possible origin of the broad thermal surge in thicker ring regions is emphasized. In turn, regolith properties might be inferred from the thermal phase curves in the optically thin ring regions.