  We study the evolution of magnetoresistance with temperature in thin film
bilayers consisting of platinum and the antiferromagnet Cr$_2$O$_3$ with its
easy axis out of the plane. We vary the temperature from 20 - 60{\deg}C, close
to the N\'eel temperature of Cr$_2$O$_3$ of approximately 37{\deg}C. The
magnetoresistive response is recorded during rotations of the external magnetic
field in three mutually orthogonal planes. A large magnetoresistance having a
symmetry consistent with a positive spin Hall magnetoresistance is observed in
the paramagnetic phase of the Cr$_2$O$_3$, which however vanishes when cooling
to below the N\'eel temperature. Comparing to analogous experiments in a
Gd$_3$Ga$_5$O$_{12}$/Pt heterostructure, we conclude that a paramagnetic field
induced magnetization in the insulator is not sufficient to explain the
observed magnetoresistance. We speculate that the type of magnetic moments at
the interface qualitatively impacts the spin angular momentum transfer, with
the $3d$ moments of Cr sinking angular momentum much more efficiently as
compared to the more localized $4f$ moments of Gd.
