It has been shown that a compact, partly unfolded state of apomyoglobin, which is obtained in acidic solutions, had a heat capacity lower than that of the unfolded polypeptide chain. With increasing temperature, this intermediate state unfolds in a rather narrow temperature region. Its unfolding is accompanied by an increase of the heat capacity, which reaches the value specific for the fully unfolded polypeptide chain having all groups exposed to water. This unfolding, however, proceeds without the excess heat absorption expected for a temperature induced two-state transition. This eliminates the possibility of considering this process as a first order phase transition, as gross conformational transitions in proteins are usually considered. It appears that the process of unfolding of the intermediate state of apomyoglobin might represent a second order phase transition, which has been predicted on theoretical grounds for those compact proteins without unique structure, known as "molten globules".