  We consider the QCD scattering amplitudes at high energies sqrt{s} and fixed
momentum transfers sqrt{-t} in the leading logarithmic approximation at a
non-zero temperature T in the t-channel. It is shown that the BFKL Hamiltonian
has the property of holomorphic separability. The Pomeron wave function for
arbitrary T is calculated using an integral of motion. In multi-colour QCD, the
holomorphic Hamiltonian for n-reggeized gluons at temperature T is shown to
coincide with the local Hamiltonian of an integrable Heisenberg model and can
be obtained from the T=0 Hamiltonian by an unitary transformation. We discuss
the wave functions and the spectrum of intercepts for the colourless reggeon
states.
