The use of contrastive loss for representation learning has become prominent in computer vision, and it is now getting attention in Natural Language Processing (NLP).Here, we explore the idea of using a batch-softmax contrastive loss when fine-tuning large-scale pre-trained transformer models to learn better task-specific sentence embeddings for pairwise sentence scoring tasks. We introduce and study a number of variations in the calculation of the loss as well as in the overall training procedure; in particular, we find that a special data shuffling can be quite important. Our experimental results show sizable improvements on a number of datasets and pairwise sentence scoring tasks including classification, ranking, and regression. Finally, we offer detailed analysis and discussion, which should be useful for researchers aiming to explore the utility of contrastive loss in NLP.