Theoretical and computational kinetics approaches are applied to thermal dissociation reactions of trapped gas-phase ions at very low pressures, where infrared-radiative ion activation dominates over collisions. Reaction rates and temperature dependences are most accurately interpreted by master-equation kinetic modeling. A more qualitative but physically understandable alternative using the truncated Boltzmann distribution is also presented and is chiefly useful for interpreting the Arrhenius activation energy to obtain an estimate of the ion dissociation energy. The theory is quantified and illustrated at 300 K by detailed calculations using a generic model of typical hydrocarbon ions with sizes ranging from 30 to 300 internal degrees of freedom. Ions with bond strengths around 0.5 eV (or somewhat higher for larger ions) are expected to dissociate with time constants of a few seconds to a few minutes. Kinetic shift effects should not be important for ions with less than about 50 atoms. These conceptual and quantitative considerations show that the experimental observation of IR-radiation-induced, thermal dissociation of ions on a time scale of seconds is expected, and indeed inevitable, at pressures below the limit of collisional interference.