Indoor inspection robots operating in occupied buildings need to minimize disturbance to occupants and access high areas of a room and cramped spaces obstructed by obstacles for higher inspection coverage. However, existing indoor inspection robots are still unable to meet these requirements. This paper aims to explore the feasibility of applying wall-climbing robots to address these requirements. To this end, we propose a small-sized wall-climbing robot prototype that can move on common indoor surfaces. We extend the proposed prototype to support thermographic inspection by integrating thermal imaging technology into it. Experiment results show that the proposed robot prototype can reach more wall and floor areas for inspection than previously developed indoor inspection robots. It has also been demonstrated that the reduced size and the wall-climbing ability allow the robot to largely avoid human activity areas, thereby reducing disturbance to occupants. This study represents the first attempt to introduce wall-climbing robots into the indoor inspection domain and provides the initial validation of their advantages over existing indoor inspection robots regarding improving inspection coverage and minimizing disturbance to occupants. The findings in this study can provide valuable insights for the future design, selection and application of robotic systems for indoor inspection tasks.