We present high resolution heat capacity data in the temperature range 30–300 K for several homogeneous samples of the superconductor Tl2Ba2CuO6 (“2201”) with transition temperatures in the vicinity of 90 K. The specific heat peaks that appear close to the superconducting transition in some samples are identified as being due to gases trapped in the pores of the ceramics. The very small intrinsic anomaly at Tc, of the order of 1% of the total specific heat, is best observed in samples prepared under He atmosphere. The data are analysed using a model that includes a parametrized phonon spectrum, a mean-field jump at Tc, and a fluctuation contribution of the Lawrence-Doniach type. The fit yields an average coherence length of 7.5 Å (sample with Tc =92 K) and 8.2 Å (sample with Tc=87 K), and a vanishingly small mean-field jump. The homogeneity of the electronic subsystem is questioned. The data are compared with new results for Bi2Sr2CaCu2O8 (“2212”, Tc=93 K) and YBa2Cu3O7 (“123”, Tc=91 K). The fluctuation component is similar for all three, but YBa2Cu3O7 stands out with its relatively large mean-field jump.