I'd planned this for the weekend, but since the weather was so windy and wet I saved it until today. I started a small fire using a couple of handfulls of wood offcuts and paper, and kept it going in the dome for about an hour and a half before leaving the embers to cool. Thanks to my new thermometer I could see that the temperature got up to about 220C at the inner surface of the dome, and about 180C an inch into the dome. The hearth brick never got much above 80C - the thermocouple in the hearth insulation never changed from its starting temperature.
The unsurprising part is that the dome cracked a little (early on, after about 30 min), but only hairline cracks that run all the way around the dome, and down the back of the dome. You can't see them from the inside, and they didn't leak any smoke. I don't think they'll be a problem.
This was a big step forwards - it works! I'm particularly pleased with the chimney - no smoke out the front at all - all went straight up. One happy builder.