We investigate the role of Compton heating in radiation-regulated accretion on to black holes from a neutral dense medium using 1D radiation-hydrodynamic simulations . We focus on the relative effects of Compton-heating and photo-heating as a function of the spectral slope \alpha , assuming a power-law spectrum in the energy range of 13.6 eV– 100 keV . While Compton heating is dominant only close to the black hole , it can reduce the accretion rate to 0.1 % ( l \propto \dot { m } ^ { 2 } model ) – 0.01 % ( l \propto \dot { m } model ) of the Bondi accretion rate when the BH radiation is hard ( \alpha \sim 1 ) , where l and \dot { m } are the luminosity and accretion rate normalised by Eddington rates , respectively . The oscillatory behaviour otherwise typically seen in simulations with \alpha > 1 , become suppressed when \alpha \sim 1 only for the l \propto \dot { m } model . The relative importance of the Compton heating over photo-heating decreases and the oscillatory behaviour becomes stronger as the spectrum softens . When the spectrum is soft ( \alpha > 1.5 ) , photo-heating prevails regardless of models making the effect of Compton heating negligible . On the scale of the ionization front , where the gas supply into the Strömgren sphere from large scale is regulated , photo-heating dominates . Our simulations show consistent results with the advection-dominated accretion flow ( l \propto \dot { m } ^ { 2 } ) where the accretion is inefficient and the spectrum is hard ( \alpha \sim 1 ) .