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The bilayer perovskite Sr$_3$Ru$_2$O$_7$ has been widely studied as acanonical strange metal. It exhibits $T$-linear resistivity and a $T\log(1/T)$electronic specific heat in a field-tuned quantum critical fan. Criticality isknown to occur in `hot' Fermi pockets with a high density of states close tothe Fermi energy. We show that while these hot pockets occupy a small fractionof the Brillouin zone, they are responsible for the anomalous transport andthermodynamics of the material. Specifically, a scattering process in which twoelectrons from the large, `cold' Fermi surfaces scatter into one hot and onecold electron renders the ostensibly non-critical cold fermions a marginalFermi liquid. From this fact the transport and thermodynamic phase diagram isreproduced in detail. Finally, we show that the same scattering mechanism intohot electrons that are instead localized near a two-dimensional van Hovesingularity explains the anomalous transport observed in strainedSr$_2$RuO$_4$.

Theory of the Strange Metal Sr$_3$Ru$_2$O$_7$