  We propose a pyroelectric energy conversion device that converts heat
directly to electricity. In contrast to conventional pyroelectric energy
conversion designs, this energy harvesting system is detached from any external
power sources, operating only under periodically varying temperature. Such
detachment unambiguously attributes the converted electricity to heat that
drives the change of polarization in the pyroelectric material, not to the
electric field alternation caused by the external battery. Using pure and Zr
doped BaTiO$_3$, we demonstrate the electricity generation in consecutive
temperature cycles. We further develop a thermodynamic model for the energy
conversion system. Our model suggests that the work output is rate dependent:
the work output per cycle is linearly dependent on the heat/cooling frequency
below the predicted threshold. The linearity is confirmed by experiments, and
the threshold frequency is derived by theory. Finally we propose a figure of
merit that separates the materials intrinsic properties from the system design
parameters. The figure of merit guides the future material development and
device improvement. Our work clears out confusions and reforms the foundation
for pyroelectric materials' resurgence as a competitor for green electricity.
