Semi-conjugate and fully-conjugate computational fluid dynamic investigations of the flow and heat transfer in a 25 L pilot-scale unbaffled stirred tank reactor with a plain jacket are reported. A hot heat transfer fluid (DW-Therm) flows through the plain jacket and heats water in the vessel, which is agitated by a pitched three-blade impeller. The shape of the free-surface of the vortex formed in the unbaffled vessel is captured by the use of a homogeneous multiphase and free-surface flow model. The simulations of flow and heat transfer are carried out using the ANSYS CFX (V.15) code. The semi-conjugate simulation considers the vessel wall and the vessel contents, and the fully-conjugate simulation also includes the flow in the jacket. The upward flow in the jacket is uneven and this dominates the distributions of heat transfer coefficients and shear stresses on the inner and outer surfaces of the vessel wall. The downward motion created by the impeller generates very high heat transfer on the base surface of the vessel, but this is nullified by a stagnation zone in the base region of the jacket. Overall heat transfer coefficients evaluated from average film heat transfer coefficients values from the simulations are around 15 % higher than those evaluated from correlations in the literature. In this pilot plant facility, the combined thermal resistances for the convection in the jacket and across the glass wall dominate the overall heat transfer coefficient.