We present the results of a 55 ks NuSTAR observation of the core of the Coma Cluster. The global spectrum can be explained by thermal gas emission, with a conservative 90% upper limit to non-thermal inverse Compton (IC) emission of 5.1 × 10-12 erg cm-2 s-1 in a 12' × 12' field of view. The brightness of the thermal component in this central region does not allow more stringent upper limits on the IC component when compared with non-imaging instruments with much larger fields of view where claims of detections have been made. Future mosaic NuSTAR observations of Coma will further address this issue. The temperature map shows a relatively uniform temperature distribution with a gradient from the hot northwest side to the cooler southeast, in agreement with previous measurements. The temperature determination is robust given the flat effective area and low background in the 3-20 keV band, making NuSTAR an ideal instrument to measure high temperatures in the intracluster medium.