We have mapped four massive cores in Orion using the NH3 (J,K)=(1,1) and (J,K)=(2,2) inversion transitions as part of our effort to study the pre-protostellar phase of massive star formation. These cores were selected to be quiescent; i.e., they contain no apparent IR sources and are not associated with any molecular outflows. These cores are 1 order of magnitude more massive than dark cloud cores and have about twice the line width. This paper focuses on their temperature structure. We find a statistically significant correlation between the gas kinetic temperature and the gas column density. The general trend is for the gas to be colder where the column density is higher, which we interpret to mean that the interiors of these cores are colder than the regions surrounding them. This is in contrast with dark cloud cores, which exhibit relatively flat temperature profiles. The temperature gradient within the massive quiescent Orion cores is consistent with an external radiation source heating the dust and dust-gas collisions providing relatively close coupling between dust and gas temperatures. Thus, we suggest that the initial stage of massive pre-protostellar cloud cores is relatively quiescent condensations that are cooler than their surroundings.