Thermoluminescence (TL) probes the emission of luminescence associated with the de-trapping of a radical pair as the temperature is increased. This technique has proved useful for characterizing the energetic arrangement of cofactors in photosynthetic reaction centers. In the original TL theory, stemming from solid-state physics, the radical pair recombination was considered to coincide with the light-emitting process. In photosynthetic systems, however, recombination takes place through various routes among which the radiative pathway generally represents a relatively minor leak, and the theoretical framework must be modified accordingly. The radiative route is the one with the largest activation energy and is thus (still) more disfavored at low temperature, so that during the heating process, the TL peak tends to lag behind the decay of the radical pair. A consequence is that the integrated luminescence emission increases with the heating rate. In this article, we examine how the characteristics of the TL emission depend on the redox potentials of the cofactors, showing good agreement between theory and experimental studies on Photosystem (PS) II mutants. We also analyze the effect on (thermo-) luminescence of the connectivity of the light-harvesting pigment antenna, and show that while this should affect significantly luminescence kinetics at room temperature, the effect on TL is expected to be small.