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In this paper, we study the finite-temperature quantum fluctuation of aclassical liquid induced by the topology of an effective conical spacetime, aswell as by a quasi-periodic boundary condition. The conical spacetime could beeither a disclination or a cosmic string. In this context, we consider a phononfield representing quantum excitations of the liquid density, which obeys aneffective Klein- Gordon equation with the sound velocity replaced by the lightvelocity. We obtain closed analytic expressions for the thermal Hadamardfunction, and consequently, the renormalized mean square density fluctuation ofthe liquid along with thermodynamics quantities such as internal energy, freeenergy, total energy, and entropy densities. We also discuss the limitingcases, including low and high-temperature regimes, and the situations in whichthere are only either the conical spacetime or quasi-periodicity.

Thermal Casimir effect in a classical liquid in a quasi-periodically identified conical spacetime