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Starting from an analytical expression for the Helmholtz free energy wecalculate the thermal corrections to the Casimir energy-density and entropywithin nearby ideal parallel plates in the vacuum of a massless scalar field.Our framework is the Kerr spacetime in the presence of quintessence and massivegravitons. The high and low temperature regimes are especially analysed inorder to distinguish the main contributions. For instance, in the hightemperature regime, we show that the force between the plates is repulsive andgrows with both the quintessence and the massive gravitons. Regarding theCasimir entropy, our results are in agreement with the Nernst heat theorem andtherefore confirm the third law of thermodynamics in the present scenario.

Thermal Casimir effect in Kerr spacetime with quintessence and massive gravitons