The paper provides analytical and semi-analytical solutions to predict the temperature transient behavior of a vertical well producing slightly compressible fluid under specified constant-bottom-hole pressure or rate in a two zone, radial composite no-flow reservoir system, where the inner zone could represent the skin zone, whereas the outer zone represents non-skin zone. The solutions are obtained by solving the decoupled isothermal diffusivity equation for pressure and thermal energy balance equation for temperature for the inner and outer zones by using the finite-difference and Laplace transformation. They be used to simulate temperature transient behavior for the general cases of specified variable bottom-hole or rate production represented by piecewise constants in specified time intervals. The convection, conduction, transient adiabatic expansion and Joule-Thomson heating effects are all considered in solving the temperature equation. Graphical analysis procedures for analyzing such temperature transient data jointly with pressure or rate transient data are also discussed. The results show that sandface temperature first decreases due to adiabatic expansion and then increases due to Joule-Thomson heating for both constant rate and constant bottomhole pressure production cases during infinite-acting flow. During boundary dominated flow, sandface temperature decreases linearly with time due to pore-volume expansion of the fluid over the entire no-flow reservoir system. The time rate of decline is governed by the ratio of the adiabatic-expansion coefficient of the fluid to the volumetric heat capacity of the saturated medium and the pore volume. However, these flow regimes are not well-defined for the constant bottomhole production case because the sandface rate decreases continuously during the infinite-acting radial flow and boundary dominated flow periods and distorts the flow regimes which are well defined on the temperature behavior if the well were produced at a constant rate. Sandface temperature data under specified variable rate or bottom-hole pressure show complicated behaviors and require more general automated history matching methods based on simultaneous use of both sandface temperature and rate transient data sets for parameter estimation.