The thermal conductivity of model argon nanowires over a wide range of temperatures from 20 K to 70 K has been calculated using the formula obtained by solving the Boltzmann equation and independently by molecular dynamic (MD) simulations. The theoretical predictions for thermal conductivity take into account the effect of phonon confinement and boundary scattering. Two known theoretical approaches were used. The first approach is based on the solution of the Boltzmann equation with given boundary conditions and uses bulk acoustic phonon dispersion and neglects the phonon confinement effect. The second approach includes also the modification of acoustic phonon dispersion due to spatial confinement. In simulations, the square and circular shapes of wire with the transverse size of nanowires from 4.3 nm to 42.9 nm have been considered. It was found that MD simulation results match the theoretical predictions reasonably well. The obtained results showed that the phonon confinement effect influences the thermal conductivity of nanowires, but the dominant factor decreasing the thermal conductivity with the thickness of nanowires is boundary scattering. Moreover, the values of the interface specular parameter indicate that the specular phonon-boundary scattering prevails over diffuse phonon-boundary scattering.