The linear stability of dissipative drift electrostatic modes in tokamak plasmas is studied numerically with an extended version of the gyrokinetic code [Kinezero C. Bourdelle and et al. , Nucl. Fusion 42 , 892 (2002)] including a modified Krook collision operator to account for collisional effects on the trapped electron response. This new version of Kinezero has been successfully tested and benchmarked against the results of a more sophisticated and complete gyrokinetic solver, GS2 [M. Romanelli, C. Bourdelle, and W. Dorland, Phys. Plasmas 11 , 3845 (2004)]. The critical density and temperature gradients for ion gradient driven modes ITG and trapped electron modes TEM have been computed for different values of collisionality. The threshold for TEM disappears as the collisionality increases. A detailed study of the dependence of the growth rate of the dissipative TEM on collisionality and density gradient is presented in the paper. The range of parameters where the dissipative trapped electron modes are destabilized by increasing collisionality corresponds to very steep density gradients that can hardly be achieved in today’s large tokamaks.