Social media based micro-blogging sites like Twitter have become a common source of real-time information (impacting organizations and their strategies, and are used for expressing emotions and opinions. Automated analysis of such content therefore rises in importance. To this end, we explore the viability of using deep neural networks on the specific task of emotion intensity prediction in tweets. We propose a neural architecture combining convolutional and fully connected layers in a non-sequential manner - done for the first time in context of natural language based tasks. Combined with lexicon-based features along with transfer learning, our model achieves state-of-the-art performance, outperforming the previous system by 0.044 or 4.4% Pearson correlation on the WASSA’17 EmoInt shared task dataset. We investigate the performance of deep multi-task learning models trained for all emotions at once in a unified architecture and get encouraging results. Experiments performed on evaluating correlation between emotion pairs offer interesting insights into the relationship between them.