  In the search of high-temperature superconductivity one option is to focus on
increasing the density of electronic states. Here we study both the normal and
$s$-wave superconducting state properties of periodically strained graphene,
which exhibits approximate flat bands with a high density of states, with the
flatness tunable by the strain profile. We generalize earlier results regarding
a one-dimensional harmonic strain to arbitrary periodic strain fields, and
further extend the results by calculating the superfluid weight and the
Berezinskii-Kosterlitz-Thouless (BKT) transition temperature $T_\text{BKT}$ to
determine the true transition point. By numerically solving the
self-consistency equation, we find a strongly inhomogeneous superconducting
order parameter, similarly to twisted bilayer graphene. In the flat band regime
the order parameter magnitude, critical chemical potential, critical
temperature, superfluid weight, and BKT transition temperature are all
approximately linear in the interaction strength, which suggests that
high-temperature superconductivity might be feasible in this system. We
especially show that by using realistic strain strengths $T_\text{BKT}$ can be
made much larger than in twisted bilayer graphene, if using similar interaction
strengths. We also calculate properties such as the local density of states
that could serve as experimental fingerprints for the presented model.
