The Orion Nebula (NGC 1976, M42) contains the nearest massive star forming region and is therefore ideal for studying the physical process accompanying star formation. The high spatial resolution available with HST imaging in emission lines and continuum permits highly detailed study of such processes, as has been described notably by O'Dell (2001). The unique opportunity to study proper motions has been used by O'Dell and collaborators in a succession of articles, and here we extend their work by constructing maps of proper motion velocities in several zones of the central region, using the technique of cross-correlation, to optimize the precision of the differential measurement of emission line images separated in time by ~7 years. The second piece of work reported is a search for time variability of the intensity between these images. Spatial temperature inhomogeneities ("fluctuations") are a well-known phenomenon in HII regions, affecting their use in interpretative work, especially in the derivation of abundances, but their origin has never been clearly resolved. Some possible mechanisms for producing them entail quite rapid time variations of temperature on small scales and we have looked for these using the same set of HST images as for the proper motions, in OIII, NII and Halpha with the time separation cited above. To discriminate against noise we used a digital filter which eliminated high spatial frequencies, and by comparing the difference images in different lines we could distinguish between variability due to changes in density, or temperature, or to apparent changes due to proper motions. We detected temperature variations of order 0.4% of the mean temperature, on scales of 2x10 ^-2 pc. We also noted that these were detectable in zones of minimum proper motion, while in zones with high proper motion density fluctuations could be measured.