Bimetallic balance wheels were an integral component of Harrison’s chronometers designed in the eighteenth century in an attempt to effectively discern longitudinal location. They provided a huge leap forward in accuracy. Modern materials have rendered them redundant but they can still be found swinging away in the heart of many an old watch.
A bimetallic balance is a screw balance wheel made of brass (on the outer rim) and steel (on the interior rim). Because of the differing temperature coefficients of the metals, they react differently under the influence of temperature. The steel hairspring used with these bimetallic balances is so thin it too expands and contracts under the influence of temperature. The fineness of the steel spring causes it to behave more like brass, which is far more reactive than steel (it has a higher temperature coefficient). In warm temperatures the brass will expand and pull the arms of the bimetallic balance out. This mirrors the effect an increase in temperature has on the steel hairspring. So when the temperature rises the spring AND the wheel expand so that they are still working in harmony. Similarly, under cold temperatures, the brass contracts, pulling the arms in (see diagrams below) to mirror the reaction of the hairspring. The steel component of the wheel is thick enough to not react to temperature changes (unless they are incredibly extreme). TO this end it acts as a base against which the brass can push or pull. Without the steel component of the wheel, the brass would be too reactive and flimsy and timekeeping would be atrocious.
Bimetallic balances are expensive and have fallen out of favour due to the discovery and refinement of new materials that boast a much lower temperature coefficient such as Elinvar springs, Glucydur balance wheels and, more recently, silicon.