An improved transient nonlinear finite element program was developed to solve coupled-field problems with field-dependent material properties. The program was applied to three problems: (i) Determining the tolerance of transmission class solid dielectric cable to conducting contaminants as defined by the maximum size of the worst-case metallic contaminant that will not cause failure during operation, as a function of the operating field of the cable dielectric. This problem requires computing the space charge limited field at the tip of the defect in cross-linked polyethylene, the electric conductivity of which is a function of electric field and temperature. The calculated maximum tolerable defect size agrees well with empirical data. (ii) The effect of convective heat transfer in a tank-type metal oxide surge arrester during the IEC thermal stability Type Test, during which the arrester is first heated by two current pulses that increase substantially the low field conductivity of the arrester elements (ZnO), after which an AC voltage is applied for 30 minutes to determine if the arrester will remain stable. Simulating this test requires calculating the AC power dissipation in the ZnO element stack as a function of electric field and temperature, as well as the heat dissipation through the complex thermal circuit of the arrester. Simulation results show that by increasing convective heat transfer through forced convection, the required ZnO mass can be reduced by half. (iii) The cooling effects of Al heat sinks placed between arrester elements to improve arrester thermal stability. The distribution of power dissipation in the arrester elements caused by the operating AC voltage was computed as a function of axial position and time after adiabatic heating of the arrester elements. This problem requires 2-D finite element computation of the electric and thermal fields in a highly nonlinear system. The use of heat-of-fusion heat sinks, which melt at low temperature and can 'clamp' the ZnO temperature, was also investigated.