  Observations of extended atmospheres around hot planets have generated
exciting results concerning the dynamics of escaping planetary material. The
configuration of the escaping planetary gas can result in asymmetric transit
features, producing both pre- and post-transit absorption in specific atomic
transitions. Measuring the velocity and strength of the absorption can provide
constraints on the mass loss mechanism and, potentially, clues to the
interactions between the planet and the host star. Here we present a search for
H$\alpha$ absorption in the circumplanetary environments of the hot planets
KELT-3 b and GJ 436 b. We find no evidence for absorption around either planet
at any point during the two separate transit epochs that each system was
observed. We provide upper limits on the radial extent and density of the
excited hydrogen atmospheres around both planets. The null detection for GJ 436
b contrasts with the strong Ly$\alpha$ absorption measured for the same system,
suggesting that the large cloud of neutral hydrogen is almost entirely in the
ground state. The only confirmed exoplanetary H$\alpha$ absorption to date has
been made around the active star HD 189733 b. KELT-3 and GJ 436 are less active
than HD 189733, hinting that exoplanet atmospheres exposed to EUV photons from
active stars are better suited for H$\alpha$ absorption detection.
