  The very interesting magnetic properties of frustrated magnetic molecules are
often hardly accessible due to the prohibitive size of the related Hilbert
spaces. The finite-temperature Lanczos method is able to treat spin systems for
Hilbert space sizes up to 10^9. Here we first demonstrate for exactly solvable
systems that the method is indeed accurate. Then we discuss the thermal
properties of one of the biggest magnetic molecules synthesized to date, the
icosidodecahedron with antiferromagnetically coupled spins of s=1/2. We show
how genuine quantum features such as the magnetization plateau behave as a
function of temperature.
