Transformer based language models have been widely adopted by industrial and research organisations in developing machine learning applications in the presence of limited annotated data. While these models show remarkable results, their functioning in few-shot settings is still poorly understood. Hence, we perform an investigative study to understand the characteristics of such models fine-tuned in few-shot setups. Specifically, we compare the intermediate layer representations obtained from a few-shot model and a pre-trained language model. We observe that pre-trained and few-shot models show similar representations over initial layers, whereas the later layers show a stark deviation. Based on these observations, we propose to freeze the initial Transformer layers to fine-tune the model in a constrained text classification setup with K annotated data points per class, where K ranges from 8 to 64. In our experiments across six benchmark sentence classification tasks, we discover that freezing initial 50% Transformer layers not only reduces training time but also surprisingly improves Macro F1 (upto 8%) when compared to fully trainable layers in few-shot setup. We also observe that this idea of layer freezing can very well be generalized to state-of-the-art few-shot text classification techniques, like DNNC and LM-BFF, leading to significant reduction in training time while maintaining comparable performance.