The factors affecting the thermal behavior of a lithospheric slab descending into the mantle are so numerous and complicated that only numerical methods can accurately account for them. A series of finite-difference calculations of the temperature field, including the effects of viscous dissipation, adiabatic compression, phase changes and radioactive heat generation are carried out, and the relative effects of different parameters are investigated. An analysis of the stability and convergence of the numerical method indicates that the errors are small and can be reduced to any desired level by varying the grid size and the time steps. At a crustal spreading rate of 8 cm/yr, with all heat sources, the slab reaches thermal equilibrium with the surrounding mantle at a depth of about 650 km. Among observable geophysical quantities, seismic travel times and amplitudes provide the most information about the slab. Surface heat flow is sensitive to subsurface conditions that are at relatively shallow depths, and gravity anomalies are broad and are masked by crustal effects. Three dimensional calculations predict strong bending of seismic rays near slabs, which causes strong focusing and produces shadow zones. Analysis of travel-time data for the Tonga-Fiji region indicates that waves propagating down the slab from shallow events are advanced by about 4 sec. Observations and theoretical travel-time anomalies based on calculated temperature fields are in general agreement.