The propagation equation in truncated cones with visco-thermal effects is a classical problem of the acoustics of wind instruments. It is derived in the frequency domain, at the second order of the asymptotic expansion with respect to the Stokes number. Using the generalization of the Euler equation due to Zwikker and Kosten, the transfer matrix of a truncated cone is computed. The canonical expression of the propagation equation (without term with the derivative of the first order) is shown to be extremely simple. It allows using the WKB method, which is applied at both the zeroth and the second orders. The accuracy of the results is compared to that of a numerical method based upon the division in short conical frustums with uniform visco-thermal effects. As a result, the WKB second order is very good at higher frequencies, and even the zeroth order. Conversely, at low frequencies, the errors are not negligible. The instrument considered is a simplified bassoon, because of the large amount of visco-thermal losses for very small radii and low frequencies. For this instrument, the WKB zeroth order seems to be better than the second. This is due to a slow convergence of the WKB expansion for this particular case. The zeroth order can be kept if the length of the missing cone is large compared to the wavelength. Finally, a simplified version of the zeroth order is based on the weak influence of visco-thermal effects on the value of the characteristic impedance. Its simplicity seems to be a satisfactory compromise.