Spatial maps of extreme precipitation are a critical component of flood estimation in hydrological modeling, as well as in the planning and design of important infrastructure. This is particularly relevant in countries such as Norway that have a high density of hydrological power generating facilities and are exposed to significant risk of infrastructure damage due to flooding. In this work, we estimate a spatially coherent map of the distribution of extreme hourly precipitation in Norway, in terms of return levels, by linking generalized extreme value (GEV) distributions with latent Gaussian fields in a Bayesian hierarchical model. Generalized linear models on the parameters of the GEV distribution are able to incorporate location-specific geographic and meteorological information and thereby accommodate these effects on extreme precipitation. A Gaussian field on the GEV parameters captures additional unexplained spatial heterogeneity and overcomes the sparse grid on which observations are collected. We conduct an extensive analysis of the factors that affect the GEV parameters and show that our combination is able to appropriately characterize both the spatial variability of the distribution of extreme hourly precipitation in Norway, and the associated uncertainty in these estimates.