Convolutional neural networks (CNNs) are built with convolution layers which account for most of their computation time. The differences in the convolution kernel types (2D, point-wise, depth-wise), and input sizes lead to significant differences in their computation and memory demands. In this work, we exploit run-time reconfiguration to adapt to the differences in the characteristics of different convolution kernels on a low-power reconfigurable architecture, Transmuter. The architecture consists of light-weight cores interconnected by caches and crossbars that support run-time reconfiguration between different cache modes-shared or private, different dataflow modes-systolic or parallel, and different computation mapping schemes. To achieve run-time reconfiguration, we propose a decision-tree-based engine that selects the optimal Transmuter configuration at a low cost. The proposed method is evaluated on commonly-used CNN models such as ResNetl8, VGGII, AlexNet and MobileNetV3. Simulation results show that run-time reconfiguration helps improve the energy efficiency of Transmuter in the range of 3.1 times-13.7 times across all networks.