The offshore wells are subject to hostile environments of such areas as the North Sea, GOM and the high arctic. The strong loop ocean currents and induced eddies can pose significant problems for deep-water well. Broadly divided ocean currents, surface currents, bottom currents and vertical currents, interact with the deep water well structures as one of environmental forces. One of the engineering challenges in deep water drilling is temperature gradient. In the past the temperature in the wellbore was ignored and an isothermal system was assumed because no practical means existed to determine the well bore temperature profile. But the fact is that the negative thermal gradient exists between surface to seafloor and it becomes positive below the seafloor. The extreme values could be as low as 40°F and as high as 150∼200°F. In addition to low temperature condition, the significant heat exchange also occurs for high temperature and geothermal reservoirs. The universal matrix form of implicit finite differential equations is introduced to predict the temperature profile of the fluid in the well and near-wellbore formation. This paper is to combine various factors together to derive a solver for the transient temperature modeling during the dirculation of riserless drilling, which can be the basis to describe the near-wellbore well stability under geo-thermal stress and predict the annular pressure during HPHT injection or production, which can also be used to including but not limited to the dynamic temperature profile and bottom-hole temperature, improving cementing program design, casing thermal stresses to be determined.