  We revisit the theory of tunnel-coupled atomic quasicondensates in
double-well elongated traps at finite temperatures. Using the
functional-integral approach, we calculate the relative-phase correlation
function beyond the harmonic limit of small fluctuations of the relative phase
and its conjugate relative-density variable. We show that the thermal
fluctuations of the relative phase between the two quasicondensates decrease
the frequency of Josephson oscillations and even wash out these oscillations
for small values of the tunnel coupling.
