The heat transport of surface phonon-polaritons propagating along a polar uniaxial anisotropic nanofilm is studied for different orientations of its optical axis, film thicknesses, and temperatures. For an hBN nanofilm, it is shown that i) the propagation of polaritons can be described in terms of even and odd modes that generalize the transverse magnetic and transverse electrical ones that typically appear in isotropic films. ii) The frequency spectrum of polaritons can efficiently be tuned with the angle between the film optical axis and their propagation direction. iii) The polariton thermal conductivity takes higher values for a thinner or hotter nanofilm. iv) The even and odd modes have a remarkable contribution to the total polariton thermal conductivity, which takes a value higher than 5.6 Wm−1K−1 for a 25-nm-thick nanofilm at 500 K. The obtained results thus uncover some key features of the propagation and heat transport of polaritons in uniaxial nanofilms.