  We study the behaviour of the interquark potential in lattice gauge theories
at high temperature, but still in the confining phase, and propose a new
observable which could play in this regime the same role played by the Luscher
term in the low temperature limit. This quantity is related to the exponent of
the power prefactor in the effective string partition function or,
equivalently, to the coefficient of the logarithmic correction in the
interquark potential and, as for the usual Luscher term, its value does not
depend on the particular gauge group under consideration or on the form of the
effective string action used to model the flux tube. In this respect it can be
considered as a universal signature of the effective string behaviour of the
flux tube. As a test of our proposal we studied this quantity with a set of
high-precision numerical simulations in the (2+1) dimensional SU(2), SU(3) and
SU(4) Yang-Mills theories and in the Z_2 gauge model, always finding a perfect
agreement with the predicted values.
