  We study the internal state dynamics of optically trapped polyatomic
molecules subject to room temperature blackbody radiation. Using rate equations
that account for radiative decay and blackbody excitation between rovibrational
levels of the electronic ground state, we model the microscopic behavior of the
molecules' thermalization with their environment. As an application of the
model, we describe in detail the procedure used to determine the blackbody and
radiative lifetimes of low-lying vibrational states in ultracold CaOH
molecules, the values of which were reported in previous work [Hallas et al.,
arXiv:2208.13762]. Ab initio calculations are performed and are found to agree
with the measured values. Vibrational state lifetimes for several other
laser-coolable molecules, including SrOH and YbOH, are also calculated.
