In this paper, we present a model to investigate the evolution of fluid and rock temperature during fluid circulation in a wellbore. The analysis considers circulation of a fluid down a centralized drill or tubing string with the returned fluid travelling up the annular space between the tubing and the wellbore. Under such conditions, which typically occur during drilling, the cooler injected fluid is heated as it travels down the tubing and cools the wellbore rock as it returns up the annulus. Based on the established governing equations for heat transfer between fluid and rock, a semi-analytic method is developed by applying Laplace transformation and numerical inversion to find the results in time and space. The heat transfer coefficients between rock and fluid are dependent on flow behaviour and material properties, characterizing advective heat transfer under complex flow. A dimensional analysis is conducted to identify the controlling dimensionless parameters. The solutions are validated by comparisons with theoretical predictions of heat diffusion inside the rock and with measured downhole temperature variations. The results show that the injection rate plays an important role in the downhole temperature evolution. The surface outlet temperature of the fluid from the annulus typically reaches a pseudo-steady state in a relatively rapid manner. Additionally, the strong cooling resulting from injection of cold fluid with circulation back up the annulus may cause significant thermoelastic changes in rock stress near the wellbore, potentially leading to tensile hydraulic fracturing initiation. Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.