The extreme operating conditions in deepwater drilling lead to serious relative problems. The knowledge of subsea temperatures is of prime interest to petroleum engineers and geo-technologists alike. Petroleum engineers are interested in subsea temperatures to better understand geo-mechanisms; such as diagenesis of sediments, formation of hydrocarbons, genesis and emplacement of magmatic formation of mineral deposits, and crustal deformations. Petroleum engineers are interested in studies of subsurface heat flows. The knowledge of subsurface temperature to properly design the drilling and completion programs and to facilitate accurate log interpretation is necessary. For petroleum engineers, this knowledge is valuable in the proper exploitation of hydrocarbon resources. This research analyzed the thermal process in drilling or completion process. The research presented two analytical methods to determine temperature profile for onshore drilling and numerical methods for offshore drilling during circulating fluid down the drillstring and for the annulus. Finite difference discretization was also introduced to predict the temperature for steady-state in conventional riser drilling and riserless drilling. This research provided a powerful tool for the thermal analysis of wellbore and rheology design of fluid with Visual Basic and Matlab simulators.