Transport properties of fluids can be determined efficiently from non-equilibrium molecular dynamics simulations using the two-gradient method which was introduced recently. It is shown here that thermal and caloric properties of fluids can also be determined accurately and efficiently along with the transport properties using this method. In a single run, all these properties are obtained for a series of state points at different temperatures and constant pressure. The truncated and shifted Lennard-Jones fluid is studied here as a test case. Data are reported for about 700 state points in the range of T = [0.7, 8.5] and ρ = [0.2, 1.0]. Besides data on the thermal conductivity, shear viscosity, and self-diffusion, the following thermal and caloric properties were measured: pressure p, internal energy u, enthalpy h, isobaric heat capacity c p, and thermal expansion coefficient α p. The results of the thermal and caloric properties agree very well with those from an accurate equation of state from the literature. Also the shear rate dependence of these properties can be studied easily with the two-gradient method.