Macroscopic modelling of heal transfer in composites in the presence of interfacial thermal resistance is determined from a description at the heterogeneity scale using a method of double-scale asymptotic developments. The analysis shows five different models. Their domains of validity are defined by the value of a dimensionless parameter. That permits the determination of the correct model for a given macroscopic boundary value problem. The models for a binary composite are shown to belong to two main types : one-temperature and two-temperature field models.