Anakwor Farlorn
Nope. Even if they do connect to somewhere on the surface, for a heat storm to come from it, means that anything that came out of the tunnels into the city would have already fried. 300-500km/h is fast, but it's not instant, and not feasible in this scenario. Even if it was, if it made it all the way from the explosion site to the viceroy mansion, it means everyone between those two points would be crispy chicken right now as well.
As to wether the dome is hermatically sealed or not, is not up to us. The CIS side has posted that there's a gate with guards on the outside that people use if I'm not mistaken, but as there's no submission for it anywhere, there's not something we can point at and claim to be an indisputable fact.