A thermographic non-destructive inspection conducted during the winter season on precious walls confined to an indoor environment (Baiocco room, L’Aquila, Italy) is illustrated herein. The use of a heat conveyor ad hoc selected has produced a particular benefit in terms of defect detection after the application of advanced algorithms because the thermal stimulus coming from an air heater hit the finishing layer under a laminar flow regime. Thermocouples registered both the heat-up and cool-down phases to confirm the numerical simulations conducted via Comsol Multiphysics® software. The results obtained by applying the principal component thermography (PCT) technique to raw data registered in the time domain were a priori studied through thermographic simulations. Defects were modelled on the basis of results already shown in a previous work centred on the Baiocco room, too. A comparison between the results obtained from PCT and the innovative sparse principal component thermography (SPCT) technique was also added to the discussion. The SPCT results show their benefits above all when they are supplemented with ground-penetrating radar results. The experimental analyses were conducted on a multi-layer wall called thereafter rectangular portal, in which the instant thermal conductance was experimentally measured. Subsurface cracks were detected using a long heating-up phase. This procedure is preferred by the Monuments and Fine Arts Department with respect to the use of flash lamps. Indeed, short energy pulses should be avoided on finishing layers having low emissivity values because producing spurious reflections affecting the thermographic results. A discussion on this point is also provided. On the basis of the data analysis, it is possible to say that the thermal waves should arrive at the interface between the masonry and its top layer in order to obtain a clear thermal map of the defects present at different depths. As shown, this goal can be realized through a smart solution based on: (a) the inverse knowledge of the aedicula via thermal analyses, (b) the best mesh to be selected for the numerical model, and (c) the optimal type of thermal stress to be delivered to the object under inspection.