We extend the thermoremanent magnetization (TRM) and pTRM theories developed in paper 1 (Dunlop and Xu, this issue) to grains in which domain walls are pinned by microcoercivities of varying magnitudes. Assuming microcoercivities to be exponentially distributed, we find that the intensity of a total TRM is linearly proportional to the inducing field Ho for small Ho, to a power of roughly 1--1/n for intermediate Ho, and independent of Ho for large Ho, similar to the results obtained in paper 1. Here n represents the temperature dependence of microcoercivity that goes as the nth power of the saturation magnetization MS(T). The above three field dependent regions correspond to thermally blocked, field-blocked, and reequilibrated walls, respectively. When being thermally demagnetized, a TRM induced in a high field has low unblocking temperatures, as observed. For a partial TRM acquired from T2(To, an even higher T2 is required. In such cases, the room temperature intensity of pTRM is approximately proportional to Ho2 when Ho is small. The resulting thermal demagnetization curve, normalized to the intensity before heating, is independent of both Ho and the mean value of microcoercivities. Complete demagnetization will not occur at a demagnetizing temperature T2 but only at a temperature close to Tc. The theory is supported by experimental data of thermal demagnetizations of pTRMs measured for various multidomain magnetite samples. ¿ American Geophysical Union 1994