  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 holomorphic Hamiltonian for
n-reggeized gluons at temperature T is shown to be obtained from the T=0
Hamiltonian by an unitary transformation. The connection with field
quantization in accelerated frames and black hole backgrounds is discussed. The
effect of the running of alpha_{QCD} on the pomeron eigenvalues is
investigated.
