A new model is proposed for an aging viscoelastic material. The medium is treated as a collection of springs instantly joining the system or collapsing so that their total number is fixed at all times. A new constitutive equation is suggested for the case of a thermoviscoelastic solid. It is assumed that the rate of “birth” of new springs \(r\) in the medium is proportional to its temperature \(\theta\). Under this assumption, the destruction rate \(w\) and the dimensionless rate of birth \(v\) are unique solutions of a linear Volterra equation. The proposed model is claimed to be in better agreement with the real physical process of non-isothermal loading as indicated by experimental data.