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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. ΔT(MJ) ≈ 0.013-0.020, ΔT(BT) ≈ 0.018-0.026, and ΔT(BFKV) ≈ 0.006-0.013 (in reduced unit). Unlike MJ and BT potentials, results from the BFKV potential show an anomaly where the magnitude of R(g) decreases on raising the temperature in a range ΔT(A) ≈ 0.015-0.018 before reaching its steady-state random coil configuration. Scaling of the structure factor, S(q) ∝ q(-1/ν), with the wave vector, q=2π/λ, and the wavelength, λ, reveals a systematic change in the effective dimension (D(e)∼1/ν) of the histone with all potentials (MJ, BT, BFKV): D(e)∼3 in the globular structure with D(e)∼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.