We present high-spectral-resolution L-band (2.91–3.85 μm) observations of the warm Neptune GJ 436 b from Keck II/KPIC. KPIC’s single-mode fiber feed reduces the L-band background by a factor of 30, significantly improving sensitivity compared to a seeing-limited spectrometer and enabling a tentative (signal-to-noise ratio of 3–4) cross-correlation detection of GJ 436 b with a thermally inverted atmospheric model. In contrast with recent results from JWST and high-resolution transmission spectroscopy, our retrieval analysis prefers the presence of H2O, and possibly CH4, molecular features in emission. The broadband continuum flux associated with the maximum-likelihood model is substantially higher than expected based on both the ∼670 K equilibrium temperature of GJ 436 b and previous results from low-resolution spectroscopy. We demonstrate that the loss of continuum information during the processing of high-resolution spectra makes our analysis effectively insensitive to the absolute continuum level of the planet, and that scaling the maximum-likelihood model to match the broadband flux measured from low-resolution observations of GJ 436 b results in a detection of similar strength in cross correlation. These results could be explained by a thermal inversion arising above a haze layer in the upper atmosphere of GJ 436 b. Further observations, ideally posteclipse in order to break the Kp–Δvsys degeneracy, are needed to clarify this possible detection. This work demonstrates the potential of L-band high-resolution spectroscopy for characterizing significantly smaller and cooler exoplanets compared with hot Jupiters.