Core-annular flow of two immiscible fluids provides attractive means for the transportation of heavy oils. This paper presents an exact analytical solution of thermal entry problems in hydrodynamically fully-developed laminar core-annular flow in a circular pipe. Both first-kind and third-kind boundary conditions are considered. The eigenvalue problem in the two-layer composite medium is solved by using the sign-count method. The local Nusselt number in the thermal entry region depends on the dimensionless longitudinal coordinate, the Biot number, the interface location, and property ratios. Numerical results of the local and asymptotic Nusselt numbers are presented for typical two-phase flow parameters and different Biot numbers.