A review of dissipative cosmology supports the application of the full causal theory of bulk viscosity. It is shown that truncated versions of this theory lead, under many conditions, to pathological behaviour of the temperature. The thermodynamical consistency of viscous fluid inflation is discussed. Dissipative de Sitter inflationary solutions are given, in which the viscosity is lower than for the non-causal or truncated solutions, and the inflation rate is different. It is possible, in principle, to generate the right amount of entropy without re-heating, given an inflation of about 60 e-folds at a rate of about 6 x 1033s-1 .