• Two nonlinear flow regimes (Forchheimer and low-velocity nonlinear) are identified in rough fractures under HTHM conditions.
• Higher temperatures and lower roughness enhance fluid flow and nonlinearity at low confining pressures.
• A modified Forchheimer equation incorporating contact area ratio and thermal expansion coefficient accurately predicts nonlinear flow.
• Findings provide critical insights for deep oil/gas extraction and hydraulic fracturing design.