The structure of a protein (H2AX) as a function of temperature is examined by three knowledge-based phenomenological interactions, MJ (Miyazawa and Jernigan), BT (Betancourt and Thirumalai), and BFKV (Bastolla et al.) to identify similarities and differences in results. Data from the BT and BFKV residue-residue interactions verify finding with the MJ interaction, i.e., the radius of gyration (Rg ) of H2AX depends non-monotonically on temperature. The increase in Rg is followed by a decay on raising the temperature with a maximum at a characteristic value, Tc , which depends on the knowledge-based contact matrix, TcBFKV ≤ TcMJ ≤ TcBT . The range (ΔT) of non-monotonic thermal response and its decay pattern with the temperature are sensitive to interaction. A rather narrow temperature range of ΔTMJ ≈ 0.015-0.022 with the MJ interaction expands and shifts up to ΔTBT ≈ 0.018-0.30 at higher temperatures with the BT interaction and shifts down with the BFKV interaction to ΔTBFKV ≈ 0.011-0.018. The scaling of the structure factor with the wave vector reveals that the structure of the protein undergoes a transformation from a random coil at high temperature to a globular conformation at low temperatures.