There were braziers enough to warm us in the courtyard, not to mention the warming effects of exploding blackpowder in our faces. Unless the tunnels are weirdly cold, I think you're good - not to mention if the tunnels were cold all these tortured people would be frozen solid. Unless they're all being iron maiden'd while being wrapped in goose-down duvets!

But ain't no disrespect in asking to be sure.