An improved constitutive model is proposed in which the time space upper-convected derivative is used to characterize heat conduction phenomena. The space Riesz fractional Cattaneo-Christov model is the generalization of Fourier law which takes the effects of relaxation time, fractional parameter and convection velocity into account. Formulated governing equation possesses the coexisting characteristics of parabolic and hyperbolic. Solutions are obtained numerically by the shifted Grunwald formula for space fractional derivatives and the theoretical analyses are presented for special cases. Three interesting characteristics are found: (a) for spatial evolution, the distribution is symmetrical for u = 0 while asymmetrical for u not equal 0. (b) fot temporal evolution, the distribution is oscillating decreasing for zeta not equal 0 but monotone decreasing for zeta = 0. (c) for fractional parameters evolution, the distribution is approximately linearly descending. Moreover, the influences of the involved parameters on the temperature distribution are also shown graphically and discussed in detail. (C) 2016 Elsevier Ltd. All rights reserved.