In order to investigate compressive mechanical behaviors of rock materials after different heating-cooling treatments, in this paper, a series of uniaxial compressive experiments are carried out on red sandstone samples after various heating temperature (from 25℃ to 1000℃) and water cooling treatments (10℃) to obtain evolution laws of mechanical property. The evolution laws of peak strength, elastic modulus, primary wave velocity and micro-structure are analyzed in details. And for better reflecting compressive stress-strain behaviors of red sandstone after heating-cooling treatments, based on Caputo variable-order fractional calculus, considering strain correlation and constant strain loading rate, we propose a novel variable-order fractional constitutive model to describe stress-strain behaviors of red sandstone samples after heating-cooling treatments. The validation of proposed model is well verified and a comparative study between proposed variable-order fractional constitutive model and constant-order fractional constitutive model is performed to highlight the advantage of proposed model. The evolutions of mechanical characteristics are revealed by presented varying-order function related to strain and the influence of fitting parameters on stress-strain behaviors are also discussed for deeply comprehending compressive mechanical mechanism of red sandstone after heating-cooling treatments.