TEMLOPI/V.2: a computer program for estimation of fully transient temperatures in geothermal wells during circulation and shut-in. This paper describes the development, validation and application of the TEMLOPI/V.2 computer program. This program is a useful tool for estimating in-situ the transient temperature distribution of the fluids employed for drilling geothermal wells. TEMLOPI/V.2 is based on a mathematical model which is developed to consider two-dimensional transient heat transfer during drilling and shut-in conditions in and around a geothermal well. The solution of the partial differential equations is based on the finite-difference technique with an implicit scheme. This scheme serves to demonstrate the numerical solution procedure. Each radial grid node is placed in a different thermal region: flow inside the pipe, metal pipe wall, flow inside annulus, and the surrounding formation. The program was written in FORTRAN 77 using modular programming and runs on most IBM compatible personal computers. The software code, its architecture, input and output files, the solution algorithm, flow diagrams and source programs are described in detail. From validation tests, computed temperatures differ by less than 5°C from analytically obtained temperatures. Comparison of results from the fully transient TEMLOPI/V.2 simulator and the pseudo-transient version, TEMLOPI/V.1, with measured data shows that the fully transient model provides better results. Application of TEMLOPI/V.2 is demonstrated in a practical application study of well EAZ-2 from Los Azufres Mexican geothermal field.