Abstract: We have measured the magnetic field and temperature dependence of specific heat in Bi2Sr2-xLaxCuO6 single crystals over wide doping and temperature regions. The superconductivity related specific heat coefficient γsc and entropy have been determined. It is found that γsc has a hump-like anomaly at Tc and exhibits a long tail which persists far into the normal state for the underdoped samples, but for the heavily overdoped samples it ends sharply just near Tc. Interestingly, we found that the entropy associated with superconductivity is almost conserved when and only when the long tail part in the normal state is taken into account for the underdoped samples, indicating the presence of residual superconductivity above Tc.