In this work, with the help of a semi-classical two-dimensional Monte Carlo (MC) simulator, we study the DC current-voltage curves of Self-Switching Diodes (SSDs) fabricated on an AlGaN/GaN heterostructure from 100 K up to room temperature. Due to the very narrow channel of the SSDs, the presence of surface effects plays a key role not only on their DC behavior but also on their RF detection performance. The evolution with temperature of the negative surface charge density σ at the etched sidewalls of the SSD is the key quantity to explain the measurements. At 300 K, MC simulations with a constant value of σ are able to replicate very satisfactorily the experiments. However, to reproduce the shape of the I-V curve at low temperatures, a more realistic approach, where σ depends not only on T, but also on the applied bias V, is necessary.