  The temperature and electric field dependence of electronic contribution to
the thermal conductivity (TC) of a granular superconductor is considered within
a 3D model of inductive Josephson junction arrays. In addition to a
low-temperature maximum of zero-field TC K(T,0) (controlled by mutual
inductance L_0 and normal state resistivity R_n), the model predicts two major
effects in applied electric field: (i) decrease of the linear TC, and (ii)
giant enhancement of the nonlinear (i.e., grad T-dependent) TC with
[K(T,E)-K(T,0)]/K(T,0) reaching 500% for parallel electric fields E=E_T
(E_T=S_0|grad T| is an "intrinsic" thermoelectric field). A possiblity of
experimental observation of the predicted effects in granular superconductors
is discussed.
