The IT and FT values for coal and coke samples can be accurately predicted by applying equations to determine ST and HT temperatures. For reducing atmospheres, the equations are IT=C1×ST−C2×HT+C3 and FT=C4×HT−C5×ST+C6. For oxidizing atmospheres, the equations are IT=C7×ST−C8×HT+C9 and FT=C10×HT−C11×ST+C12. IT is the initial deformation temperature. ST is the softening temperature. HT is the hemispherical temperature. FT is the fluid temperature. C1-C12 are constants determined by multi-linear regression coefficient analytical techniques on a collection of data.