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