the exact shape of this tail may reflect details of the specific area chosen for study, the fact that the T$_{p}$ correlation is consistently higher and the δT$_{p}$ – Δ cross correlation also extends to this distance indicates that the process by which the gap collapses is more sensitive to the surround- ing several nanometers than the process that sets the gap energy scale. We have performed the first detailed mea- surements of the temperature evolution of the superconducting gap for a large number of points in overdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+}$$_{δ}$. Due to dopants and crystalline disorder, the ten- dency toward pairing is natrually inhomoge- neous. Correspondingly, the superconducting gap is also inhomogeneous, albeit smoothed out by interactions between regions. The temper- ature evolution is also inhomogeneous, but we have found that the compared to the gap the magnitude of its variation is more and the length scale of its variation is shorter, that is, the tem- perature evolution is even more smoothed out. Also, regions of the sample with a small gap magnitude can have this gap survive to higher temperatures if surrounded by larger gapped re- gions. We speculate that the closing of the gap may have to do not just with thermal pair- breaking, but also with phase fluctuations, so that regions bordered by larger gapped regions have the phase pinned up to a higher temper- ature than similar regions bordered by small gapped regions. ∗ Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA † Current Address: Department of Physics, Stan- ford University, Stanford, CA 94305, USA [1] K. K. Gomes, A. N. Pasupathy, A. Pushp, S. Ono, Y. Ando, and A. Yazdani, Nature 447 , 569 (2007). [2] C. Howald, P. Fournier, and A. Kapitulnik, Physical Review B 64 , 100504(R) (2001). [3] S. H. Pan, J. P. O’Neal, R. L. Badzey, C. Cha- mon, H. Ding, J. R. Engelbrecht, Z. Wang, H. Eisaki, S. Uchida, A. K. Gupta, et al., Na- ture 413 , 282 (2001). [4] K. McElroy, J. Lee, J. Slezak, D. Lee, H. Eisaki, S. Uchida, and J. Davis, Science 309 , 1048 (2005). [5] I. Bozovic, G. Logvenov, M. A. J. Verhoeven, P. Caputo, E. Goldobin, and M. R. Beasley, Physical Review Letters 93 , 157002 (2004). [6] O. Yuli, I. Asulin, O. Millo, D. Orgad, L. Iomin, and G. Koren, Physical Review Let- ters 101 , 057005 (2008). [7] E. Berg, D. Orgad, and S. A. Kivelson, Physi- cal Review B 78 , 094509 (2008). [8] A. Gozar, G. Logvenov, L. F. Kourkoutis, A. T. Bollinger, L. A. Giannuzzi, D. A. Muller, and I. Bozovic, Nature 455 , 782 (2008). [9] V. Kresin, Y. Ovchinnikov, and S. Wolf, Physics Reports 431 , 231 (2006). 7