  We study nonperturbative interaction corrections to the thermodynamic
quantities of multichannel disordered wires in the presence of the Coulomb
interactions. Within the replica nonlinear $\sigma$-model (NL$\sigma$M)
formalism, they arise from nonperturbative soliton saddle points of the
NL$\sigma$M action. The problem is reduced to evaluating the partition function
of a replicated classical one dimensional Coulomb gas. The state of the latter
depends on two parameters: the number of transverse channels in the wire,
N_{ch}, and the dimensionless conductance, G(L_T), of a wire segment of length
equal to the thermal diffusion length, L_T. At relatively high temperatures,
$G(L_T) \gtrsim \ln N_{ch} $, the gas is dimerized, i.e. consists of bound
neutral pairs. At lower temperatures, $\ln N_{ch} \gtrsim G(L_T) \gtrsim 1$,
the pairs overlap and form a Coulomb plasma. The crossover between the two
regimes occurs at a parametrically large conductance $G(L_T) \sim \ln N_{ch}$,
and may be studied independently from the perturbative effects. Specializing to
the high temperature regime, we obtain the leading nonperturbative correction
to the wire heat capacity. Its ratio to the heat capacity for noninteracting
electrons, C_0, is $\delta C/C_0\sim N_{ch}G^2(L_T)e^{-2G(L_T)}$.
