Convolutional Neural Networks (ConvNets) can be shrunk to fit embedded CPUs adopted on mobile end-nodes, like smartphones or drones. The deployment onto such devices encompasses several algorithmic level optimizations, e.g., topology restructuring, pruning, and quantization, that reduce the complexity of the network, ensuring less resource usage and hence higher speed. Several studies revealed remarkable performance, paving the way towards real-time inference on low power cores. However, continuous execution at maximum speed is quite unrealistic due to a fast increase of the on-chip temperature. Indeed, proper thermal management is paramount to guarantee silicon reliability and a safe user experience. Power management schemes, like voltage lowering and frequency scaling, are common knobs to control the thermal stability. Obviously, this implies a performance degradation, often not considered during the training and optimization stages. The objective of this work is to present the performance assessment of embedded ConvNets under thermal management. Our study covers the behavior of two control policies, namely reactive and proactive, implemented through the Dynamic Voltage-Frequency Scaling (DVFS) mechanism available on commercial embedded CPUs. As benchmarks, we used four state-of-the-art ConvNets for computer vision flashed into the ARM Cortex-A15 CPU. With the collected results, we aim to show the existing temperature-performance trade-off and give a more realistic analysis of the maximum performance achievable. Moreover, we empirically demonstrate the strict relationship between the on-chip thermal behavior and the hyper-parameters of the ConvNet, revealing optimization margins for a thermal-aware design of neural network layers.