We present first-principles studies of the thermopower of the organometallic V₄Bz₅ molecule attached between Co electrodes with noncollinear magnetization directions. Different regimes in the formation of the noncollinear magnetic state of the molecule lead to a remarkable nonmonotonous dependence of the thermopower on the angle between the magnetizations of the electrodes. This complex behavior is explained by the resonant properties of the electron transmission. Consequently, the nanocontacts can be utilized for local heating or cooling controlled by the external magnetic field.