This paper presents a study of the thermal transport properties of MgB2 tapes differing in architecture, stabilization and constituent materials. The temperature and field dependence of thermal conductivity, $kappa(T,B)$, was investigated both along the conductor and in the direction perpendicular to the tape. These data provide fundamental input parameters to describe the 3D heat diffusion process in a winding. Thermal transport properties—even in field—are typically deduced using semi-empirical formulas based on the residual resistivity ratio of the stabilizer measured in absence of magnetic field. The accuracy of these procedures was evaluated comparing the calculated κ values with the measured ones. Based on the experimental thermal conduction properties $kappa(T,B)$ and critical current surface ${J}_{{ m{C}}}(T,B)$ we determined the dependence of minimum quench energy and normal zone propagation velocity on the operating parameters of the conductor. The correlation between thermal properties and tape layout allowed us to provide information on how to optimize the thermal stability of MgB2 conductors.