The response of electric devices to an applied thermal gradient has, so far, been studied almost exclusively in two-terminal devices. Here we present measurements of the response to a thermal bias of a four-terminal, quasiballistic junction with a central scattering site. We find a novel transverse thermovoltage measured across isothermal contacts. Using a multiterminal scattering model extended to the weakly nonlinear voltage regime, we show that the device's response to a thermal bias can be predicted from its nonlinear response to an electric bias. Our approach forms a foundation for the discovery and understanding of advanced, nonlocal, thermoelectric phenomena that in the future may lead to novel thermoelectric device concepts.