Heated shot requires a broadly appropriately tuned gun system, to the target range and consistency. If the shot passes through and through it does nothing additional. If it hits rigging or spars it will nearly always pass through with no additional damage. Heated shot lodged in timbers can cause a localised heating and fire - maybe - if it can be got at the fire can be prevented by driving the shot out and applying water. Heated shot which passes into the gun deck can cause problems - it isn't localised heat, so fires to structure are unlikely (IMO), but the issues of injury to crew are increased by the high temperature of the shot - generally shot rolling on the deck are dangerous anyway (even just 'rolling' can break feet and ankles, with 'spent shot' amputating the feet of soldiers trying to stop it with a foot being a known phenomena in land warfare with 3-12pdr shot) - but the greatest risk it to the small supply of powder on the gundeck. I would treat each hit with heated shot on the gun deck as a test for "bursting a gun" or some similar rule, but at a 1 in 'some' chance ~ 1 in 6 or 2 in 6.

Lodging in timber, or worse passing into the Hold &/or Magazine can cause a fire or explosion. Frigates at (iirc) Tripoli were not harmed by hot shot, because the gunners were using distance charges from 18-24pdr guns, which passed through and through at close ranges. Had the charges been moderated the risk to the ships could have been more serious.