This paper is concerned with numerical simulations of a pyroelectric converter for direct energy conversion of waste heat into electricity. The simulated prototypical device consisted of a hot and cold source separated by a series of vertical microchannels supporting pyroelectric thin films made of co-polymer P(VDF-TrFE) and undergoing the Olsen cycle. A piston was used to vertically oscillate a working fluid back and forth between the thermal sources. The experimental device was instrumented with thermocouples and a pressure sensor. The two-dimensional transient mass, momentum, and energy equations were solved numerically using finite element methods to determine the local and time-dependent temperature at various locations inside the device microchannels. The operating frequency varied from 0.025 to 0.123 Hz and the working fluid was 1.5 or 50 cSt silicone oil. Good agreement was found between the simulated and experimentally measured local mean temperatures for both working fluids at all operating frequencies considered. The local temperature swings were underestimated slightly for 50 cSt silicone oil and significantly more for 1.5 cSt silicone oil. Overall, this study confirms our previous numerical results. Moreover, this numerical model could be used to design and operate the next generation of pyroelectric energy converters based on oscillatory convective heat transfer.