For investigating the microscopic description of non-equilibrium steady states (NESSs), it is important to examine the properties of the NESSs by using concrete models. We discuss temperature gradients in an open and non-uniform spin--1/2 XXZ chain contacting with 2 reservoirs at different temperatures. The non-uniformness is introduced by the random $xx$--coupling given by the Gaussian distribution. The density operator evolves in time according to the Lindblad type quantum master equation. We numerically obtain the NESSs and discuss their temperature profiles. We statistically analyze the relation between the fluctuation of the $xx$--coupling and 1) the temperature difference of the spins in the boundary, 2) the smoothness of the temperature profile. We clarify that there exist crossovers from flat to smooth temperature profile, and from smooth to jumped profile.