  The interaction of two--level atoms with a common heat bath leads to an
effective interaction between the atoms, such that with time the internal
degrees of the atoms become correlated or even entangled. If part of the atoms
remain unobserved this creates additional indirect decoherence for the selected
atoms, on top of the direct decoherence due to the interaction with the heat
bath. I show that indirect decoherence can drastically increase and even
dominate the decoherence for sufficiently large times. I investigate indirect
decoherence through thermal black body radiation quantitatively for atoms
trapped at regular positions in an optical lattice as well as for atoms at
random positions in a cold gas, and show how indirect coherence can be
controlled or even suppressed through experimentally accessible parameters.
