  We study a class of integrable alternating (S1,S2) quantum spin chains with
critical ground state properties. Our main result is the description of the
thermal Drude weight of the one-dimensional alternating spin chain as a
function of temperature. We have identified the thermal current of the model
with alternating spins as one of the conserved currents underlying the
integrability. This allows for the derivation of a finite set of non-linear
integral equations for the thermal conductivity. Numerical solutions to the
integral equations are presented for specific cases of the spins S1 and S2. In
the low-temperature limit a universal picture evolves where the thermal Drude
weight is proportional to temperature T and central charge c.
