  The specific heat of two polymorphs of BaPd2As2 was measured. The
ThCr2Si2-type polymorph (space group I4/mmm, $D_{4h}^{17}$, No. 139) is a
previously reported superconductor with a transition temperature Tc $\simeq$
3.5 K, while the CeMg2Si2-type polymorph (P4/mmm, $D_{4h}^{1}$, No. 123) is a
normal metal and does not exhibit superconductivity down to 1.8 K. Our results
revealed that the ThCr2Si2-type has an anomalously low Debye temperature,
indicative of soft phonons, compared to the CeMg2Si2-type. Moreover, a large
specific-heat jump at Tc indicated that the superconductivity of ThCr2Si2-type
is a strong-coupling type, which is likely derived from soft phonons.
