Hot Rocks Survey I : A possible shallow eclipse for LHS 1478 b

M dwarf systems offer an opportunity to study terrestrial exoplanetary atmospheres due to their small size and cool temperatures. However, the extreme conditions imposed by these host stars raise question about whether their close-in rocky planets are able to retain any atmosphere at all. The Hot Rocks Survey aims to answer this question by targeting nine different M dwarf rocky planets. Of these, LHS 1478 b orbits an M3-type star, has an equilibrium temperature of T$_{eq}$ = 585 K and receives 21 times Earth's instellation. We observe two secondary eclipses using photometric imaging at 15$\mu$m using the Mid-Infrared Instrument on the James Webb Space Telescope (JWST MIRI) to measure thermal emission from the dayside of the planet. We compare these values to atmospheric models to evaluate potential heat transport and CO$_2$ absorption signatures. We find that a secondary eclipse depth of $138\pm 53$ppm at the expected time for a circular orbit is preferred over a null model at $2.8\sigma$, a moderate detection, though dynamical models do favour a non-eccentric orbit for this planet. The second observation results in a non-detection due to significantly larger unexplained systematics. Based on the first observation alone, we can reject the null hypothesis of the dark (zero Bond albedo) no atmosphere bare rock model with a confidence level of 3.3$\sigma$, though for $A_B=0.2$ the significance decreases to $2.1\sigma$. The tentative secondary eclipse depth is consistent with the majority of atmospheric scenarios we considered, spanning CO$_2$-rich atmospheres with surface pressures from 0.1 to 10 bar. However, we stress that the two observations from our program do not yield consistent results, and more observations are needed to verify our findings. The Hot Rocks Survey serves as a relevant primer for the Director's Discretionary Time (DDT) Rocky Worlds program.