  We demonstrate how heating of an environment can invert the line shape of a
driven cavity. We consider a superconducting coplanar cavity coupled to
multiple artificial atoms. The measured cavity transmission is characterized by
Fano-type resonances with a shape that is continuously tunable by bias current
through nearby (magnetic flux) control lines. In particular, the same
dispersive shift of the microwave cavity can be observed as a peak or a dip. We
find that this Fano-peak inversion is possible due to a tunable interference
between a microwave transmission through a background, with reactive and
dissipative properties, and through the cavity, affected by bias-current
induced heating. The background transmission occurs due to crosstalk between
the control and transmission lines. We show how such background can be
accounted for by Jaynes-Cummings type models via modified boundary conditions
between the cavity and transmission lines. We find generally that whereas
resonance positions determine system energy levels, resonance shapes give
information on system fluctuations and dissipation.
