  Thermal systems have traditionally been modeled via Euclideanized space by
analytical continuation of time to an imaginary time. We extend the concept to
static thermal gradients by recasting the temperature variation as a variation
in the Euclidean metric. We apply this prescription to determine the Quark
anti-Quark potential in a system with thermal gradient. A naturally occurring
QCD medium with thermal gradients is a Quark Gluon Plasma (QGP). However, the
QGP evolves in time. Hence, we use a quasi-stationary approximation, which is
applicable only if the rate of time evolution is slow. The application of our
proposal to a Quark anti-Quark potential in QGP can be seen as a step towards a
more exact theory which would incorporate time varying thermal gradients. The
effect of a static temperature gradient on the Quark anti-Quark potential is
analyzed using a gravity dual model. A non-uniform black string metric is
developed, by perturbing the Schwarzchild metric, which allows to incorporate
the temperature gradient in the dual AdS space. Finally, an expression for the
Quark anti-Quark potential, in the presence of a static temperature gradient,
is derived.
