  In arXiv:1403.0389 and arXiv:1610.07140 intersecting $D$-branes in flat space
were studied at finite temperature in the Yang-Mills approximation. The
one-loop correction to the tachyon mass was computed and the critical
temperature at which the tachyon becomes massless was obtained numerically. In
this paper we extend the computation of one-loop two-point amplitude to the
case of intersecting stacks of $D3$-branes in flat space. The motivation for
this calculation is to study the strong coupling holographic BCS model proposed
in arXiv:1104.2843 at finite temperature. We show that the analytical results
of arXiv:1403.0389 and arXiv:1610.07140 can be embedded into this more general
setup. The main technicality involved here is keeping track of the extra color
factors coming from the unbroken gauge groups. We further discuss the issues
involved in the computation of two point amplitude for case of multiple
intersecting stacks of branes.
