Temperature and pressure effects in two-dimensional viscoelastic flow between eccentrically rotating cylinders is investigated numerically for high eccentricities. The constitutive model employed is a White-Metzner fluid, with a viscosity and single relaxation time, both of which are shear-thinning, temperature-thinning and pressure-thickening A pseudospectral method with bipolar transformation is used for spatial discretization of the governing equations, and a first-order time stepping scheme with a filtered pressure step is used for time integration within the constraint of incompressibility. It is shown that a Dirichlet condition for temperature on the inner cylinder, coupled with a Blot (or Robbins) condition on the outer cylinder, lead to equilibrium temperature fields which have maxima in the small gap, as may be expected in journal bearing lubrication. The same effects are achieved with Blot conditions on both cylinders. It is also suggested that at high eccentricities, pressure-thickening dominates the viscosity behaviour rather than shear-thinning or temperature-thinning. Assuming that relaxation time is proportional to viscosity, this can increase the normal stresses by at least two orders of magnitude, in comparison with a constant viscosity model, resulting in increases of 20% and higher in load-bearing capacity.