I would not necessarily connect the drop of bacterial growth rate with temperature to the changes in the membrane alone. It seems that the protein stability plays a significant role in the growth/temperature dependency. The paper below describes a study on protein stability and growth temperature.
Dill, Ken A., Kingshuk Ghosh, and Jeremy D. Schmit. "Physical limits of cells and proteomes." Proceedings of the National Academy of Sciences 108.44 (2011): 17876-17882.
To answer your question more directly, I would say that in the temperature above the optimal the cell membrane becomes more permeable to protons and other ions, which would result in dissipating the membrane potential and proton motive force. Lipid composition of various psychro- meso- thermophiles is discussed in the publication below.
Russell, N. J., and N. Fukunaga. "A comparison of thermal adaptation of membrane lipids in psychrophilic and thermophilic bacteria." FEMS Microbiology Letters 75.2‐3 (1990): 171-182.
I think the membranes remain mostly intact at 45. While it is true that E. coli does not form colonies or grow at 45, I think you will find that the cells are not dead after some period of time at 45 (assuming you don't go too long). Inability to grow and divide is not the same as death.
I don't believe there is much protein denaturation at 45C, however there are a number of temperature sensitive enzymes that fail to function at 45C blocking essential pathways. So perhaps partial denaturation.