Bonded composite structures are a special type of sandwich-like structures in which multiple carbon-fibre laminates are bonded with adhesives, and debonding can appear at the bond layer due to variable loading and uncertain operating conditions. This study aims to investigate the debonding effects on Lamb wave propagation in a bonded composite structure under variable ambient temperature conditions. In the process, a combined theoretical analysis, time-domain spectral element simulation and experimental analysis of elastic wave propagation in a carbon-fibre reinforced adhesively-bonded composite structure have been carried out. It is shown that theoretical analysis and spectral formulation are effectively able to capture the behaviour of Lamb modes in the healthy structure due to variations in ambient temperature. It is found that the primary anti-symmetric Lamb wave mode amplitude and velocity decrease with an increase in ambient temperature. Furthermore, the spectral formulation accurately captures the effects of debonding on the Lamb wave signals under variable temperature conditions that are consistent with the experimental results. Finally, temperature correction factors are proposed for the primary anti-symmetric mode velocity and amplitude difference calculations and the effectiveness of the factors is successfully verified for selected study cases.