The fusion barrier distributions of 11 fusion reactions are investigated to understand the role of orientation as a degree of freedom in the fusion mechanism involving deformed nuclei, and seeking signatures of cold and hot fusion. We compared the experimentally extracted barrier distributions (BD) with those calculated using the coupled-channel method, starting from orientation-dependent folding potentials based on M3Y-Reid nucleon-nucleon interaction, with coupling to the anticipated vibrational and rotational excitations in projectile and target nuclei. We found that the signature of the hot fusion process within the compact configuration of the participating deformed nuclei is always evident in the extracted fusion barrier distribution. The different peaks appearing in the extracted BD can be individually assigned to elongated-cold or compact-hot fusion process. The imprint of the compact-hot fusion may also manifest itself as a little increase in the value of the BD at certain related energy, compared with the preceding and succeeding values.