The aim of the present work is to investigate numerically the self-heating effect (SHE) in MOSFET transistors based on high-k material taking into account the deformation of the gate under the SHE. The SHE inside the MOSFET transistor is calculated using the electrothermal model based on heat transfer equation coupled with semiconductor equations. The electrothermal model have been solved in 2D-dimension using the finite element method. The high-k dielectric HfO2 have been used as gate oxide. Several gate shapes have been used to analyze their impact on SHE. It is observed that the reduction of equivalent oxide thickness (EOT) reduces the SHE in the MOSFET transistor based in high-k dielectric material. the temperature peak increases quadratically with drain voltage for all MOSFET structures. A decrease in self-heating effect is achieved using the square gate shape.