  This paper presents a study of the thermal transport properties of MgB$_2$
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 $\kappa$
values with the measured ones. Based on the experimental thermal conduction
properties $\kappa(T,B)$ and critical current surface $J_C(T,B)$ 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 MgB$_2$ conductors.
