We study the antiferromagnetic (AFM) and structural phase transitions in single crystal BaFe 2 (As 1-x P x ) 2 ( 0, 0.3 x ) at temperatures T N and T S , respectively, by high resolution ac microcalorimetry and SQUID magnetometry. The specific heat measurements of both as grown and annealed BaFe 2 As 2 displays a sharp peak at the AFM/Structural transitions. A kink in the entropy of annealed BaFe 2 As 2 gives evidence for splitting of the two transitions by approximately 0.5K. No additional features could be identified in the specific heat of both BaFe 2 As 2 and BaFe 2 (As 0.7 P 0.3 ) 2 in the temperature regions around T* > T S where torque measurements [S. Kasahara et al., Nature 486, 382 (2012)] had revealed the "true" nematic phase transition, indicating that the behavior at T* does not represent a 2 nd order phase transition, and that the phase transition of BaFe 2 (As 1-x P x ) 2 into the orthorhombic phase does occur at T S .