A method and apparatus of reducing thermal shock in one or more radiant tubes of a pyrolysis furnace is provided. The apparatus is a furnace comprising a blower and blower bypass conduit providing separate fluid communication paths for flue gas from the convection section to a natural draft flue gas stack. The method comprises the steps of: redirecting at least a portion of the flue gas through the blower bypass conduit when a blower shut-off event is indicated as well as reducing the firing rate of the furnace.