We present direct measurements of the Peltier effect as a function of temperature from 77 to 325 K in Ni, Ni(80)Fe(20), and Fe thin films made using a suspended Si-N membrane structure. Measurement of the Seebeck effect in the same films allows us to directly test predictions of Onsager reciprocity between the Peltier and Seebeck effects. The Peltier coefficient Π is negative for both Ni and Ni(80)Fe(20) films and positive for the Fe film. The Fe film also exhibits a peak associated with the magnon drag Peltier effect. The observation of magnon drag in the Fe film verifies that the coupling between the phonon, magnon, and electron systems in the film is the same whether driven by heat current or charge current. The excellent agreement between Π values predicted using the experimentally determined Seebeck coefficient for these films and measured values offers direct experimental confirmation of the Onsager reciprocity between these thermoelectric effects in ferromagnetic thin films near room temperature.