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The von Mises yield criterion and its associated flow rule are adopted to provide the exact analytic solution for the elastic-plastic stress and strain distributions within the discs with temperature-dependent properties subject to thermal loading by a uniform temperature field and subsequent unloading. This article examines the effect of temperature-dependent properties on the size of the plastic zone. Qualitative features of the solution are emphasized. The primary objective of the article is to provide a benchmark problem having the exact analytic solution for justifying the possibility to neglect or the necessity to account for temperature-dependency of thermomechanical properties in analysis of elastic-plastic discs under plane stress conditions. [ABSTRACT FROM AUTHOR]