We present a classical approach of mixture of compressible fluids when each constituent has its own temperature. The introduction of an average temperature together with the entropy principle dictates the classical Fick law for diffusion and also new constitutive equations associated with the difference of temperatures between the components. The constitutive equations fit with results recently obtained through the Maxwellian iteration procedure in extended thermodynamics theory of multi-temperature mixtures. The differences of temperatures between the constituents imply the existence of a new dynamical pressure even if the fluids have a zero bulk viscosity.