The accurate control of the wellbore pressure not only prevents lost circulation/blowout and fracturing formation by managing the density of the drilling fluid, but also improves productivity by mitigating reservoir damage. Calculating the geothermal pressure of a geothermal well by constant parameters would easily bring big errors, as the changes of physical, rheological and thermal properties of drilling fluids with temperature are neglected. This paper researched the wellbore pressure coupling by calculating the temperature distribution with the existing model, fitting the rule of density of the drilling fluid with the temperature and establishing mathematical models to simulate the wellbore pressures, which are expressed as the variation of Equivalent Circulating Density (ECD) under different conditions. With this method, the temperature and ECDs in the wellbore of the first medium-deep geothermal well, ZK212 Yangyi Geothermal Field in Tibet, were determined, and the sensitivity analysis was simulated by assumed parameters, i.e., the circulating time, flow rate, geothermal gradient, diameters of the wellbore, rheological models and regimes. The results indicated that the geothermal gradient and flow rate were the most influential parameters on the temperature and ECD distribution, and additives added in the drilling fluid should be added carefully as they change the properties of the drilling fluid and induce the redistribution of temperature. To ensure the safe drilling and velocity of pipes tripping into the hole, the depth and diameter of the wellbore are considered to control the surge pressure.