  We study certain functions arising in the context of the calculation of
correlation functions of the XXZ spin chain and of integrable field theories
related with various scaling limits of the underlying six-vertex model. We show
that several of these functions that are related to linear integral equations
can be obtained by acting with (deformed) difference operators on a master
function $\Phi$. The latter is defined in terms of a functional equation and of
its asymptotic behavior. Concentrating on the so-called temperature case we
show that these conditions uniquely determine the high-temperature series
expansions of the master function. This provides an efficient calculation
scheme for the high-temperature expansions of the derived functions as well.
