Hydrodynamics models for inertial confinement fusion must be close by providing a law for the electron heat flux. In most non-equilibrium cases, the Spitzer-Härm local law is inadequate to account for every physical phenomena. Indeed, temperature gradients can induce non-local heat fluxes, leading to an incomplete macroscopic description. To recover this kinetic effect, an expensive kinetic equation could be solved. However, regarding practical applications, models at the mesoscopic scale reveal to be sufficient [1,2]. Specificaly, moment models allow for an accurate representation of the physics while efficiently reducing computational costs. On the other hand, such hyperbolic models make it easy to enhance the physical description (e.g., including magnetic fields). In this work, we focus on the numerical resolution of the M1 model of non-local thermal transport without magnetic fields. The multi-scale nature of this model poses numerical challenges in capturing the asymptotic bahavior associated to each flows. To address this issue, we propose using UGKS (Unified Gas Kinetic Scheme) [3], a robust asymptotic preserving scheme for the kinetic equation based on the integral solution of the kinetic equation, to elaborate the numerical fluxes. This method effectively handles both the non-local regime linked to transport (hyperbolic) and the local regime associated with diffusion (parabolic). To derive a numerical scheme for the moment model, we propose a generic approach where the UGKS numerical flux is closed with the M1 distribution function. Essentially, this technique is equivalent to projecting the distribution function onto the M1 set at each time step in UGKS. To implement this scheme, a quadrature method to compute the half-moment of the M1 distribution function on the unit sphere is presented. Moreover, a second order extension that maintains the asymptotic preserving property is proposed. Finally, this new method is validated and tested with various test cases.