Bulk samples of the nominal composition of (Tl0.6Pb0.5)(Sr0.8Ba0.2)2Ca2Cu3O8+δ−xLaO1.5 (x = 0–0.1) were prepared by using two-step process and their microstructure, T c values, and magnetization were studied. The samples consist of the Tl-1223 dominant phase with small Tl-1212 admixture, which increases with a rise of La content. Five years ageing and following oxygen annealing at 450°C and subsequently at 750°C have only a modest effect on T c values of the studied samples. Low-level La doping (x = 0:04) leads to an increase of T c values by about 2 K in comparison with undoped samples. Oxygen annealing at 750°C results in an increase in the volume magnetization hysteresis in low applied magnetic fields and rise of critical current density at zero magnetic field and 77 K. This effect is most pronounced for the low La doped sample with x = 0.04. Changes of the induced voltage, U originating in the Meissner effect and of its harmonics in dependence on temperature were measured and used for characterization of the temperature distribution of inter-grain junctions.