  A holographic description of BCS superconductivity is given in
arxiv:1104.2843. This model was constructed by insertion of a pair of D8-branes
on a D4-background. The spectrum of intersecting D8-branes has tachyonic modes
indicating an instability which is identified with the BCS instability in
superconductors. Our aim is to study the stability of the intersecting branes
under finite temperature effects. Many of the technical aspects of this problem
are captured by a simpler problem of two intersecting D1-branes on flat
background. In the simplified set-up we compute the one-loop finite temperature
corrections to the tree-level tachyon mass using the frame-work of SU(2)
Yang-Mills theory in (1 + 1)-dimensions. We show that the one-loop two-point
functions are ultraviolet finite due to cancellation of ultraviolet divergence
between the amplitudes containing bosons and fermions in the loop. The
amplitudes are found to be infrared divergent due to the presence of massless
fields in the loops. We compute the finite temperature mass correction to all
the massless fields and use these temperature dependent masses to compute the
tachyonic mass correction. We show numerically the existence of a transition
temperature at which the effective mass of the tree-level tachyons becomes
zero, thereby stabilizing the brane configuration.
