  We study the classical thermodynamics of a 1+1-dimensional double-well
sinh-Gordon theory. Remarkably, the Schrodinger-like equation resulting from
the transfer integral method is quasi-exactly solvable at several temperatures.
This allows exact calculation of the partition function and some correlation
functions above and below the short-range order (``kink'') transition, in
striking agreement with high resolution Langevin simulations. Interesting
connections with the Landau-Ginzburg and double sine-Gordon models are also
established.
