  We study the potential of $X(3872)$ at finite temperature in the
Born-Oppenheimer approximation under the assumption that it is a tetraquark. We
argue that, at large number of colors, it is a good approximation to assume
that the potential consists in a real part plus a constant imaginary term. The
real part is then computed adapting an approach by Rothkopf and Lafferty and
using as input lattice QCD determinations of the potential for hybrids. This
model allows us to qualitatively estimate at which temperature range the
formation of a heavy tetraquark is possible, and to propose a qualitative
picture for the dissociation of the state in a medium. Our approach can be
applied to other suggested internal structures for the $X(3872)$ and to other
exotic states.
