Aircraft measurements are used to characterize properties of clear-air turbulence in the lower Arctic troposphere. For typical vertical resolutions in general circulation models, there is evidence for both downgradient and countergradient vertical turbulent transport of momentum and heat in the mostly statically stable conditions within both the boundary layer and the free troposphere. Countergradient transport is enhanced in the free troposphere compared to the boundary layer. Three parametrizations are suggested to formulate the turbulent heat flux and are evaluated using the observations. The parametrization that accounts for the anisotropic nature of turbulence and buoyancy flux predicts both observed downgradient and countergradient transport of heat more accurately than those that do not. The inverse turbulent Prandtl number is found to only weakly decrease with increasing gradient Richardson number in a statistically significant way, but with large scatter in the data. The suggested parametrizations can potentially improve the performance of regional and global atmospheric models.