Galaxy clusters possess turbulent magnetic fields with a dominant scale length l_B 1-10 kpc. In the static magnetic field approximation, the thermal conductivity κ_T for heat transport over distances l_B in clusters is κ_Sl_B/L_S(ρ_e), where κ_S is the Spitzer thermal conductivity for a nonmagnetized plasma, the length L_S(r₀) is a characteristic distance that a pair of field lines separated by a distance r₀ < l_B at one location must be followed before they separate by a distance l_B, and ρ_e is the electron gyroradius. We introduce an analytic Fokker-Planck model and a numerical Monte Carlo model of field-line separation in strong magnetohydrodynamic (MHD) turbulence to calculate L_S(r₀). We also determine L_S(r₀) using direct numerical simulations of MHD turbulence with zero mean magnetic field. All three approaches, like earlier models, predict that L_S asymptotes to a value of order several l_B as r₀ is decreased toward l_d in the large-l_B/l_d limit, where l_d is the dissipation scale, which is taken to be the proton gyroradius. When the turbulence parameters used in the Fokker-Planck and Monte Carlo models are evaluated using direct numerical simulations, the Fokker-Planck model yields L_S(ρ_e) 4.5l_B and the Monte Carlo model yields L_S(ρ_e) 6.5l_B in the large-l_B/l_d limit. Extrapolating from our direct numerical simulations to the large-l_B/l_d limit, we find that L_S(ρ_e) 5l_B-10l_B, implying that κ_T 0.1κ_S-0.2κ_S in galaxy clusters in the static field approximation. We also discuss the phenomenology of thermal conduction and particle diffusion in the presence of time-varying turbulent magnetic fields. Under the questionable assumption that turbulent resistivity completely reconnects field lines on the timescale l_B/u, where u is the rms turbulent velocity, we find that κ_T is enhanced by a moderate amount relative to the static field estimate for typical cluster conditions.