A recent theory of bunch lengthening suggests that it is caused primarily by the combination of many high-frequency resonators which add up to produce an effective broad-band resistive impedance. The ultimate source is thought to be such small chamber discontinuities as vacuum flanges. Since it is the resistive component of the impedance that is responsible, the bunch lengthening should be directly correlated with the heat dissipated in these ring elements. An expression giving this correlation is derived and compared with experimental results.