We report specific-heat and resistivity experiments performed in parallel in
a Bridgman-type of pressure cell in order to investigate the nature of
pressure-induced superconductivity in the iron pnictide compound CaFe2As2. The
presence of a pronounced specific-heat anomaly at Tc reveals a bulk nature of
the superconducting state. The thermodynamic transition temperature differs
dramatically from the onset of the resistive transition. Our data indicates
that superconductivity occurs in the vicinity of a crystallographic phase
transition. We discuss the discrepancy between the two methods as caused by
strain-induced superconducting precursors formed above the bulk thermodynamic
transition due to the vicinity of the structural instability