We report the in-plane (rho (ab)) and out-of-plane (rho (c)) resistivities in the 4-800 K range on single crystals of Tl2Ba2CaCu2O8 high-T-c cuprate with T-c = 111 K (rho (c)/rho (ab) approximate to 1000). rho (ab)(T) exhibits "usual" linear behavior and rho (c)(T) follows generally metallic-like, positive slope in the 150-400 K temperature range. There is a clear crossover to semiconductor-like behavior close to T-c. However, for the first time in a chainless high-T-c cuprate we observe a crossover above 500 K due to hopping conduction. Under high pressures (< 15 kbar) the magnitude of (c) strongly decreases, yet the rho (c)(T) slope does riot change. This suggests that the out-of-plane charge transport is governed by the interplane tunneling rate.