I keep my brooder in the coop. Much nicer than keeping one in the house, but it does present a few challenges.
What I recommend is to not worry about the temperature in the entire brooder. Just keep one area in the correct temperature range and let the rest cool off as it will. I'd go batty trying to keep the entire brooder in the correct temperature range with the changing temperatures. I just keep one small area where it needs to be and let them find their comfort zone. Actually that heated area is often warmer than it should be when the outside temperature warms up during the day. I don't have temperatures as low as you are talking about when I brood, but the far corners of mine are often 20 to 30 degrees Fahrenheit cooler than the recommended temperatures. The first day or two, mine usually tend to stay real close to the heat source, but by day 3 they are roaming all over the brooder, only coming back to the heat occasionally when they need to warm up. That is not as often as you might think. And some broods start roaming the first day.
My brooder is roughly 90 cm x 150 cm and I have brooded as many as 28 chicks in it until they were about 4-1/2 weeks old. By then, they were feathered out and did not need the brooder or extra heat. It was starting to look a little crowded.
A dome might not be a bad idea. I don't use one, just make sure I have a good draft guard and use a heat lamp to heat up one spot that will stay warm. My concern with the dome is that it might get too warm. Then they won't have that gradual transition zone to find their comfort area. It would pretty quickly go from warm to cool. Maybe have that dome next to the heated area but not directly heated? I have not used them so I'm not sure how best to use one in your situation. I've seen reports on here where people that used them really like them.
As far as wattage, I can't help you. I set the brooder up ahead of time, put a thermometer under the heat lamp and adjust the height to get the right temperature at night. Then I take away the thermometer and adjust the height of the lamp based on how the chicks are acting. How the chicks react is better than any thermometer you can get. With 20 chciks, they will go a long way to keeping each other warm.
Good luck!