The surface tension and density of almost all members of the 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amides family, [C(n)mim][Ntf(2)], with 2 <= n <= 14 were measured for the first time up to 532 K and 473 K, respectively. The large number of ionic liquids studied within this family and the broad interval of working temperature enabled us to show evidence for a thermodynamic anomaly in the thermal expansivity of these ionic liquids (minima in a p versus T). The minima themselves have never been witnessed before. The data in this extended temperature range also permitted us to discuss the location of hypothetical normal boiling and critical points.