I'm in an almost similar situation. I have three chicks. The youngest is 5 weeks old. Night temperatures are in the 30s.
When I purchased the chicks from my neighborhood chicken seller/expert. He stated the that my 5 week old was good up to 40 degrees outside. He also stated, they could withstand any temperature by 4 months of age.
Then there's that rule of thumb. Drop 5 degress for every week of life. 5 week old would be about 70.
The youngest was only one week old and required a heat lamp. I kept them all together in my finished basement. I had a heat lamp for the first week and then moved them to a space heater a couple feet outside of the brooder to keep the room warm it was by a door. Over the course of many nights, I lowered the temperature of heater. I lowered the temperature of the heater all the way to 58 degrees.
Because our day temps here are up in the 60s-70s I've let them out in the pen. I've placed them in the coop with a heat lamp, chained twice, bulb dusted, cord tied. Heat lamp is two to four feet away from everything. Now I have 5, 6, and 9 week old chicks that love each other and cannot be seperated without the crying cheeps. I put them in the coop because my 9 weeker looked pitiful everytime she was put back in the brooder, she's huge and the little ones are pretty big now, feathered out. I only put the lamp on late at night and turn if off as the sun comes up to take the chill off. About 10 to 20 degree increase over outside temperature.