Embedded Convolutional Neural Networks (ConvNets) are driving the evolution of ubiquitous systems that can sense and understand the environment autonomously. Due to their high complexity, aggressive compression is needed to meet the specifications of portable end-nodes. A variety of algorithmic optimizations are available today, from custom quantization and filter pruning to modular topology scaling, which enable fine-tuning of the hyperparameters and the right balance between quality, performance and resource usage. Nonetheless, the implementation of systems capable of sustaining continuous inference over a long period is still a primary source of concern since the limited thermal design power of general-purpose embedded CPUs prevents execution at maximum speed. Neglecting this aspect may result in substantial mismatches and the violation of the design constraints. The objective of this work was to assess topology scaling as a design knob to control the performance and the thermal stability of inference engines for image classification. To this aim, we built a characterization framework to inspect both the functional (accuracy) and non-functional (latency and temperature) metrics of two ConvNet models, MobileNet and MnasNet, ported onto a commercial low-power CPU, the ARM Cortex-A15. Our investigation reveals that different latency constraints can be met even under continuous inference, yet with a severe accuracy penalty forced by thermal constraints. Moreover, we empirically demonstrate that thermal behavior does not benefit from topology scaling as the on-chip temperature still reaches critical values affecting reliability and user satisfaction.