  We have undertaken a systematic study of thermal conductivity as a function
of temperature and magnetic field of single crystals of the compound
(La$_{1-z}$Pr$_{z}$)$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ for $z$(Pr) =0.2,0.4. and
0.6. The lattice distortion due to Pr-substitution and anisotropic thermal
conductivity in bilayer manganites are discussed on the basis of different
relaxation models of local lattice distortions in metal and insulating states
proposed by Maderda et al. The giant magnetothermal effect is scaled as a
function of magnetization and discussed on the basis of a systematic variation
of the occupation of the $e_g$-electron orbital states due to Pr-substitution.
