Finite temperature expectation values of local fields in the sinh-Gordon model

Sklyanin's method of separation of variables is employed in a calculation of finite temperature expectation values. An essential element of the approach is Baxter's $Q$-function. We propose its explicit form corresponding to the ground state of the sinh-Gordon theory. With the method of separation of variables we calculate the finite temperature expectation values of the exponential fields to one-loop order of the semi-classical expansion.