We performed an experimental study of the temperature and doping dependence of the energy-loss function of the bilayer and trilayer Bi-cuprate family. The primary aim is to obtain information on the energy stored in the Coulomb interaction between the conduction electrons, on the temperature dependence thereof, and on the change of Coulomb interaction when Cooper-pairs are formed. We performed temperature-dependent ellipsometry measurements on several Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_{8-x}\) single crystals: under-doped with \(T_c=60, 70\) and 83~K, optimally doped with \(T_c=91\)~K, overdoped with \(T_c=81, 70\) and \(58\)~K, as well as optimally doped Bi\(_2\)Sr\(_2\)Ca\(_2\)Cu\(_3\)O\(_{10+x}\) with \(T_c=110\)~K. Our first observation is that, as the temperature drops through \(T_c\), the loss function in the range up to 2~eV displays an abrupt change of temperature dependence as compared to the temperature dependence in the normal state. This effect at -- or close to -- \(T_c\) depends strongly on doping, with a sign-change for weak overdoping. A second observation is that in the underdoped and optimally doped regime, when cooling down from much higher temperature, the loss function integral shows a gradual loss of spectral weight in a temperature range up to twice \(T_c\), coinciding with the range where other experiments have indicated the existence of strongly enhanced pair-correlations.