  We employ the gauge/string duality to study the thermal power terms of
various thermodynamic quantities in gauge theories and the renormalized
Polyakov loop above the deconfinement phase transition. We restrict ourselves
to the five-dimensional Einstein gravity coupled to a single scalar, the
dilaton. The asymptotic solutions of the system for a general dilaton potential
are employed to study the power contributions of various quantities. If the
dilaton is dual to the dimension-4 operator ${\rm Tr} F_{\mu\nu}^2$, no power
corrections would be generated. Then the thermal quantities approach their
asymptotic values much more quickly than those observed in lattice simulation.
When the dimension of the dual operator is different from 4, various power
terms are generated. The lowest power contributions to the thermal quantities
are always quadratic in the dilaton, while that of the Polyakov loop is linear.
As a result, the quadratic terms in inverse temperature for both the trace
anomaly and the Polyakov loop, observed in lattice simulation, cannot be
implemented consistently in the system. This is in accordance with the field
theory expectation, where no gauge-invariant operator can accommodate such
contributions. Two simple models, where the dilaton is dual to operators with
different dimensions, are studied in detail to clarify the conclusion.
