  Solutions corresponding to finite temperature (anti)-D3 and M2 branes
localised in flux backgrounds are constructed in a linear approximation. The
flux backgrounds considered are toy models for the IR of the Klebanov-Strassler
solution and its M-theory analogue, the Cveti\v{c}-Gibbons-L\"{u}-Pope
solution. Smooth solutions exist for either sign charge, in stark contrast with
the previously considered case of smeared black branes. That the singularities
of the anti-branes in the zero temperature extremal limit can be shielded
behind a finite temperature horizon indicates that the singularities are
physical and resolvable by string theory. As the charge of the branes grows
large and negative, the flux at the horizon increases without bound and
diverges in the extremal limit, which suggests a resolution via brane
polarisation \`{a} la Polchinski-Strassler. It therefore appears that the
anti-brane singularities do not indicate a problem with the SUSY-breaking
metastable states corresponding to expanded anti-brane configurations in these
backgrounds, nor with the use of these states in constructing the de Sitter
landscape.
