The long-term memory effects of gallium nitride (GaN) transistors have prevented its use in situations where the modulated envelope signal has a wide amplitude variation over time, such as in time division duplex systems. These long-term memory effects are generally attributed to electron trapping in GaN high electron-mobility transistors (HEMT), which have shown to be very difficult to compensate, especially in cellular base station transmitters known to be subjected to highly restrictive linearity specifications. On top of the electron trapping effects, we show that thermal effects can also induce long-term memory behaviors, which should also be accounted for when linearizing these devices. Because the conventional behavioral modeling approach has been incapable to compensate these long-term memory effects on GaN HEMT-based power amplifiers (PAs), we started by investigating the physical mechanisms responsible for these semiconductor impairments in GaN devices. This physics-based knowledge was then used to design new predistorter models that could effectively compensate those PAs subjected to GaN trapping and thermal effects. In this paper, we describe the new predistortion models for PA linearization, as well as the characterization methods used to determine their parameters. To validate the linearization effectiveness of the proposed model, several high power GaN-based PAs are tested with multicarrier GSM signals, and their linearization results are compared against other state-of-the-art models, evidencing a clear and significant improvement. In fact, to the authors' knowledge, the proposed approach is the first one to reduce the PA distortion effects due to GaN long-term memory effects to such low levels, allowing a comfortable compliance with the imposed linearity masks.