The primary and secondary pyroelectric coefficients were determined for binary (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) and ternary Pb(In1/2Nb1/2)O3- Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PIN-PMN-PT) relaxor-PT single crystals. The secondary pyroelectric coefficients were calculated from the thermodynamic inter-relationship between the piezoelectric, elastic, and thermal expansion coefficients. Poling along  and  directions resulted in single-domain state of "1R" and "1T" and a macroscopic symmetry of 3m and 4mm for rhombohedral (x = 0.28) and tetragonal (x = 0.42) crystals, respectively, enabling relatively large values of pyroelectric coefficients p ≥ 5.7 × 10-4 C/m2 K. The calculated results show that the secondary pyroelectric coefficients are in the range of (-0.62 ∼ -1.06) × 10-4 C/m2 K for rhombohedral crystals and (0.70 ∼ 1.14) × 10-4 C/m2 K for tetragonal crystals, significantly lower than that of primary pyroelectric coefficients, which is important for thermal directional and imaging applications. In contrast, high d15 piezoelectric coefficients (>2000 pC/N), together with zero pyroelectric coefficients in thickness shear crystals, also makes them promising candidates for piezoelectric sensors where thermal noise is undesirable. © 2013 AIP Publishing LLC.