Two characteristics of floating ice plates which are important in engineering problems are the effect of temperature on the mechanical properties of ice, and the viscoelastic response of ice under prolonged loading. In this paper, the floating ice plate is considered as a viscoelastic plate on an elastic foundation. The viscoelastic response functions are temperature dependent, and the temperature is a function of time and depth. Thermal stresses are also taken into account. The plate equations are derived from the three-dimensional theory of linear viscoelasticity. In the derivation, the thickness of the plate is considered significant, and the vertical shear stresses are retained. The resulting equation for the deflection thus differs from the classical plate equation. A solution to the plate equations is obtained for the case in which a plate adhering to a circular pile is deformed by a change in the water level.