The linear coupled theory of thermoelasticity, with a modified Fourier heat-conduction law to include the thermal-relaxation effect, has been applied in studying heat pulses in solids at very low reference temperatureT0. The theory is limited to the case in which the temperature change ∣T−T0∣ is much less than To. This restriction is relaxed in this work by developing a theory in terms of the coldness, which is the reciprocal of the temperature; in any heating process the net change in coldness is always less than the coldness at the reference state. Linear and nonlinear constitutive equations in terms of the coldness variable as well as the balance equations are proposed. They might be useful for investigating heat-pulse propagation in solids at extremely low temperature.