As the importance of adhesive bonding in modern industries is increasing, so too is is the need for material models describing the adhesives‘ behavior. Therefore, this paper examines a relatively soft polyurethane adhesive characterized by showing nonlinear viscoelastic behavior at room temperature and enduring large deformations. It is well suited for applications under dynamic loadings and can compensate gap changes generated by materials with different thermal expansion coefficients. An adhesive‘s curing process is usually activated either through elevated temperatures or through the diffusion of water and the subsequent chemical reaction. Theoretically, the examined one-component polyurethane adhesive can be cured both thermally and through humidity, resulting in the same mechanical characteristics. Comparing both curing reactions, humidity curing is much slower than thermal curing. The latter can be controlled through the applied heating rate, which may be increased to up to 150 Kmin--1. However, in comparison with metals polyurethane conducts the heat with a much smaller rate which results in high temperature gradients within the adhesive layer. This paper focuses on the modeling of a fast-curing polyurethane adhesive under consideration of the thermo-mechanical material properties induced by thermal curing. Therefore, the material properties need to be observed throughout the thermal curing process, from the uncured fluid to the cured rubber material.