  In this paper we report a detailed analysis of the temperature-dependent
optical properties of epitaxially grown cadmium arsenide (Cd$_3$As$_2$), a
newly discovered three-dimensional Dirac semimetal. Dynamic Fermi level tuning
-- instigated from Pauli-blocking in the linear Dirac cone -- and varying Drude
response, generate large variations in the mid and far-infrared optical
properties. We demonstrate thermo-optic shifts larger than those of traditional
III-V semiconductors, which we attribute to the obtained large thermal
expansion coefficient as revealed by first-principles calculations. Electron
scattering rate, plasma frequency edge, Fermi level shift, optical
conductivity, and electron effective mass analysis of Cd$_3$As$_2$ thin-films
are quantified and discussed in detail. Our ab initio density functional study
and experimental analysis of epitaxially grown Cd$_3$As$_2$ promise
applications for nanophotonic and nanoelectronic devices, such as
reconfigurable metamaterials and metasurfaces, nanoscale thermal emitters, and
on-chip directional antennas.
