  We investigate the sensitivity of solar neutrino data to mixing of sterile
neutrinos with masses $\gtrsim$ eV. For current data, we perform a
Feldman-Cousins analysis to derive a robust limit on the sterile neutrino
mixing. The solar neutrino limit excludes significant regions of the parameter
space relevant to hints from reactor and radioactive gallium source
experiments. We then study the sensitivity of upcoming solar neutrino data,
most notably elastic neutrino-electron scattering in the DARWIN and DUNE
experiments as well as coherent neutrino-nucleus scattering in DARWIN. These
high precision measurements will increase the sensitivity to sterile neutrino
mixing by about a factor of 4.5 compared to present limits. As a by-product, we
introduce a simplified solar neutrino analysis using only four data points: the
low- and high-energy $\nu_e$ survival and transition probabilities. We show
that this simplified analysis is in excellent agreement with a full solar
neutrino analysis; it is very easy to handle numerically and can be applied to
any new physics model in which the energy dependence of the $\nu_e$ transition
probabilities is not significantly modified.
