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We discuss the Casimir effect for massless scalar fields subject to theDirichlet boundary conditions on the parallel plates at finite temperature inthe presence of one fractal extra compactified dimension. We obtain the Casimirenergy density with the help of the regularization of multiple zeta functionwith one arbitrary exponent and further the renormalized Casimir energy densityinvolving the thermal corrections. It is found that when the temperature issufficiently high, the sign of the Casimir energy remains negative no matterhow great the scale dimension $\delta$ is within its allowed region. We deriveand calculate the Casimir force between the parallel plates affected by thefractal additional compactified dimension and surrounding temperature. Thestronger thermal influence leads the force to be stronger. The nature of theCasimir force keeps attractive.

The Casimir effect for parallel plates at finite temperature in the presence of one fractal extra compactified dimension