  In heat exchangers, an incompressible fluid is heated initially and cooled at
the boundary. The goal is to transfer the heat to the boundary as efficiently
as possible. In this paper we study a related steady version of this problem
where a steadily stirred fluid is uniformly heated in the interior and cooled
on the boundary. For a given large P\'eclet number, how should one stir to
minimize some norm of the temperature? This version of the problem was
previously studied by Marcotte, Doering et al. (SIAM Appl. Math '18) in a disk,
where the authors showed that when the P\'eclet number, $\mathrm{Pe}$, is
sufficiently large one can stir the fluid in a manner that ensures the total
heat is $O(1/\mathrm{Pe})$. In this paper we instead study the problem on an
infinite strip. By forming standard convection rolls we show that one can stir
the fluid in a manner that ensures that the temperature of the hottest point is
$O(1/\mathrm{Pe}^{4/7})$, up to a logarithmic factor. The same upper bound is
expected to be true for the total heat and other $L^p$-norms of the
temperature. We do not, however, know if this is optimal in a strip and are
presently unable to prove a matching lower bound.
