A detailed thermo-optic model combining the 1D transfer matrix method and a 3D finite element method is developed and used to simulate a widely tunable vernier laser based on surface etched slots. The model is used to investigate the experimentally observed tuning patterns. At low injection currents, carrier tuning dominates, while at high currents, thermal tuning is the dominant mechanism. These lasers are very simple to fabricate and have a wide tuning over 50 nm, but SMSR and linewidth performance is not yet optimised. Simulations give an insight into the observed tuning efficiency and linewidth performance of the lasers, with high carrier densities in the grating regions being identified as a key area, which is presently limiting these parameters.