The noise energy of conventional thin‐film dc superconducting quantum interference devices (SQUIDs) flattened out as the operating temperature was lowered below 140 mK. We attribute this saturation to the heating of the electrons in the resistive shunts by the SQUID bias current. This ‘‘hot‐electron effect’’ is a general property of normal metals at low temperatures and arises from the limited rate at which the electrons can transfer energy to phonons. The temperature of the electrons, and hence the noise energy of the SQUIDs, was reduced by a factor of about 3 by attaching large volume ‘‘cooling fins’’ to each shunt.