Does partial transfer learning require a lot of computer power?
The dataset on which VGG16 is trained consists of images from different domains, and its purpose is to classify images by extracting images' feature maps and attributes. Unfreezing few botton layers will help in training them for our specific image usage, however, these will be few parameters to learn than the whole connected network as it will have already learned basic features.

When you choose to train only a few bottom layers of VGG16, it will definitely require less computation.