It's already been mentioned that certain liquid-solid phase transitions are accompanied by negative thermal expansion (NTE). This also includes elements ($\ce{Si, Ga, Ge, Sb, Bi, Pu}$), alloys (Wood's metal) and numerous materials (zeolites, quartz, tugstates etc.) that obey virial expansion due to the way atoms are packed in a crystal lattice:
$$\frac{p}{RT} = \frac{1}{V_m} + \frac{B_{2V}(T)}{V_m^2} + \frac{B_{3V}(T)}{V_m^3} + \ldots$$
where $p$ - pressure, $R$ - gas constant, $T$ - temperature, $B_{iV}(T)$ - $i$-virial coefficient, $V_m$ - molar volume.
There is also another physicochemical phenomenon called Gough–Joule effect. If mechanical stress is applied to the elastomer or rubber string which is subsequently heated, the polymer contracts as a result of the intensive growth of the role of the entropy factor (the maximum entropy in polymers occurs in the coil-like ordering of the molecules). This effect is also utilized in the rubber-band heat engine (Feynman wheel).