Hydraulic tests are commonly performed prior to reservoir stimulation to determine the natural permeability of the enhanced geothermal system (EGS), which typically involves injection of cold water at low rates into the hot target EGS reservoir and measurement of the surface pressure, flow rate, and thermal drawdown simultaneously. Interpretation and analysis of the data collected during a hydraulic test are largely based on fitting type curves generated from analytical solutions. We have formulated a geomechanical model for hydraulic tests in a thermoporoelastic EGS reservoir in which the open-hole section of the borehole wall is subjected to a constant-rate flux and convective cooling. We derive the analytical solutions for injection induced axisymmetric deformation, temperature drawdown, pore pressure, and stresses in the Laplace domain, and we obtain time-domain solutions using the Stehfest inversion algorithm. We evaluate numerical examples to illustrate the competition between the thermoelastic effect and the poroelastic effect in controlling temperature, pore pressure, and stresses around the borehole wall. The numerical results indicate that temperature drawdown at the borehole wall would be significantly overestimated if a constant temperature boundary condition instead of convective cooling is used. At early times, injection induced hoop stress/pore pressure is partially offset by the corresponding ones induced by convective cooling. At late times, convective cooling plays a marginal role in influencing pore pressure and stress around the borehole. The analytical solutions are helpful to address the thermohydromechanical coupling mechanisms controlling pressure perturbations during hydraulic tests conducted in an EGS reservoir.