As has been said in the comment, there is no theoretical proof which validates $d$-wave pairing (or symmetry of the gap parameter) for the moment. But you can expand the order parameter to get higher angular momentum, and try to find the higher critical temperature associated to a given angular momentum.
More details can be found in the review
Sigrist, M., & Ueda, K. (1991). Phenomenological theory of unconventional superconductivity. Reviews of Modern Physics, 63(2), 239–311. http://dx.doi.org/10.1103/RevModPhys.63.239
Mineev, V. P., & Samokhin, K. (1998). Introduction to unconventionnal superconductivity. Gordon and Breach Science Publishers.
You can also try to find some experimental evidence for $d$-wave pairing. They usually involve some interference effect (also called phase sensitive or Josephson effect sometimes). These experiments are reviewed in the references already cited in the comment:
Van Harlingen, D. J. (1995). Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors—Evidence for dx2-y2 symmetry. Reviews of Modern Physics, 67(2), 515–535. http://dx.doi.org/10.1103/RevModPhys.67.515
Tsuei, C. C., & Kirtley, J. R. (2000). Pairing symmetry in cuprate superconductors. Reviews of Modern Physics, 72(4), 969–1016. http://dx.doi.org/10.1103/RevModPhys.72.969