When the heater coils become plugged, about the only way to clear them is to cut some of the return bends off and hydro-blast the coil to remove the coke zthat was deposited.
If you have a process temperature a few rows back from the heater outlet, remove that thermowell and hydro-blast from there. If not, cut a return bend that is three or four rows up from the outlet and begin hydro-blasting from there. I was involved in using an inspection company to determine the extent of coke formation with some success.