The influence of tidal heating on the evolution of globular clusters (GC's) in circular orbits about the Galactic center is studied. Giant Molecular Clouds (GMC's) stretch a globular cluster in a direction transverse to its orbit through the disk. The variation in acceleration with height in the disk compresses the cluster in a longititudinal direction. Numerical and analytic calculations of heating and mass loss for GC's, represented by King models, show that disk heating dominates. We apply the results to calculate GC evolution prior to core collapse or tidal disruption using a three parameter (energy, mass, and tidal radius) sequence of King models. The changes in the parameters are calculated for tidal perturbations, relaxation and evaporation. Clusters close to the Galactic center (less than 3 kpc) undergo core collapse in a Hubble time. The effect of tidal perturbations on energy and mass loss of the cluster is strongest between 3 and 5 kpc where it can substantially effect the evolution of the cluster. Here, depending upon their initial concentration, clusters are either tidally heated and dissolved, or forced towards a gravothermal catastrophe in times that are a fraction of a Hubble time. These inner regions of the Galaxy should be fertile territory for the search for post-collapsed clusters.