A properly built RMH will have vertical stack temperatures of 140F- 250F
I have seen my J tube hit 350F a few times, after 12-14 hrs of non-stop burning... when it was -10F outside.
I regularly use HVAC pipe in my RMH builds, in the mass and going up to the roof. I only use black stove pipe where it exits the mass or is a high traffic area.
Your chimney sweep is correct, any conventional
wood stove would melt the HVAC pipe quickly.