They need a proper safe, warm place to grow out. Where that place is doesn't matter.
Most folks have constructed a large box and call it their brooder. They keep one end of the box warm with a heat lamp, but all other areas of the brooder to be very cool. Chicks need to self regulate their body temperature. Having the entire brooder 90F is tough on them.
I take our chicks out to the barn at 4 weeks, typically. I do supply them with a 90 watt bulb lamp for another few weeks. Slowing weaning them off of the lamp. Our nights are still very, very cold. By 6-7 weeks, they're all feathered in and don't sleep under the lamp at all, so I pull the lamp and they go on about their business.
So much depends on the ambient air temps your local climate experiences this time of year. For certain, chicks at 5-6 weeks are simply not fragile anymore.
-depends upon the climate. We moved our chicks outdoors to the coop at about 6-7 weeks. (This, however, was at the end of April - last year - in Texas. It was already pretty warm and they were feathered out.)