The effect of temperature on the conformation of a histone (H3.1) is studied by a coarse-grained Monte Carlo simulation based on three knowledge-based contact potentials (MJ, BT, BFKV). Despite unique energy and mobility profiles of its residues, the histone H3.1 undergoes a systematic (possibly continuous) structural transition from a random coil to a globular conformation on reducing the temperature. The range over which such a systematic response in variation of the radius of gyration (R-g) with the temperature (T) occurs, however, depends on the potential, i.e. Delta T-MJ approximate to 0.013-0.020, Delta T-BT approximate to 0.018-0.026, and Delta T-BFKV approximate to 0.006-0.013 (in reduced unit). Unlike MJ and BT potentials, results from the BFKV potential show an anomaly where the magnitude of Rg decreases on raising the temperature in a range Delta T-A approximate to 0.015-0.018 before reaching its steady-state random coil configuration. Scaling of the structure factor, S(q) infinity q(-1/nu), with the wave vector, q = 2 pi/lambda, and the wavelength, lambda, reveals a systematic change in the effective dimension (D-e similar to/nu) of the histone with all potentials (MJ, BT, BFKV): D-e similar to 3 in the globular structure with D-e similar to 2 for the random coil. Reproducibility of the general yet unique (monotonic) structural transition of the protein H3.1 with the temperature (in contrast to non-monotonic structural response of a similar but different protein H2AX) with three interaction sets shows that the knowledge-based contact potential is viable tool to investigate structural response of proteins. Caution should be exercise with the quantitative comparisons due to differences in transition regimes with these interactions.