Majority of the studies on modeling the evolution of a social network using spectral graph kernels do not consider temporal effects while estimating the kernel parameters. As a result, such kernels fail to capture structural properties of the evolution over the time. In this paper, we propose temporal spectral graph kernels of four popular graph kernels namely path counting, triangle closing, exponential and neumann. Their responses in predicting future growth of the network have been investigated in detail, using two large datasets namely Facebook and DBLP. It is evident from various experimental setups that the proposed temporal spectral graph kernels outperform all of their non-temporal counterparts in predicting future growth of the networks. Copyright 2014 ACM.