  This paper presents an analysis of three-dimensional vector currents and
temperatures observed in a sunspot from the photosphere to the chromosphere,
spanning a range of heights of approximately 1500 km. With this unique dataset,
based on novel spectro-polarimetric observations of the 850 nm spectral region,
it is possible to conduct for the first time an empirical study of the relation
between currents and chromospheric heating. It is shown that, while resistive
current dissipation contributes to heat the sunspot chromosphere, it is not the
dominant factor. The heating effect of current dissipation is more important in
the penumbra of the sunspot, but even there it is still a relatively modest
contribution.
