Thermoelectric generation is an essential function in future energy-saving technologies. However, it has so far been an exclusive feature of electric conductors, a situation which limits its application; conduction electrons are often problematic in the thermal design of devices. Here we report electric voltage generation from heat flowing in an insulator. We reveal that, despite the absence of conduction electrons, the magnetic insulator LaY(2)Fe(5)O(12) can convert a heat flow into a spin voltage. Attached Pt films can then transform this spin voltage into an electric voltage as a result of the inverse spin Hall effect. The experimental results require us to introduce a thermally activated interface spin exchange between LaY(2)Fe(5)O(12) and Pt. Our findings extend the range of potential materials for thermoelectric applications and provide a crucial piece of information for understanding the physics of the spin Seebeck effect.