Neutral beam heated H-mode DIII-D and JET expanded boundary divertor discharges were examined to study the parametric dependence of the thermal energy confinement on the plasma current, plasma size and neutral beam power. Single-null discharges in both machines were examined during the ELM-free phase (ELM stands for edge localized mode) to extract information about the intrinsic H-mode thermal energy confinement time tau-th. A power law dependence of ELM-free thermal energy confinement was assumed, with the result that for B(T) almost-equal-to 2.2 T and kappa = 1.8, tau-th = C I(p)1.03 +/- 0.07 P(L)-0.46 +/- 0.06 L 1.48 +/- 0.09. The size dependence of tau-th is described by the linear dimension L since the determination of the individual dependences on the minor and major radii is precluded by the similar aspect ratio of the two machines. For this representation of tau-th (units of s, MA, MW and m), when L is the plasma major radius, C = 0.106 +/- 0.011, and when L is the plasma minor radius, C = 0.441 +/- 0.044. A dimensionally correct version of the scaling, consistent with the constraints of a collisional high beta model, is tau-th alpha I(p)1.06 P(L)-0.45 L 1.40 n(e)0.07 B(T)0.06. These results indicate that, within the experimental error, the empirical scaling and the dimensionally correct scaling are the same.