Mine out in the sun on occasion with temps in the low 50's.
Of course, as they are in black pots in black trays, the roots never get that cold.
I usually try to harden off starting the process in partial shade and light breezes, but no chance of that this year----started too early.
It's really a watch and wait game.
In full sun, watch till they just begin to stress, then bring them back in.
Reason being, it takes the roots longer to cool off and heat back up.
You don't want the roots and the greenery stressed out at the same time.
Every day it will take a tittle longer.
This week, temps are in the high 60's, I leave them out for 6 hours---and they are a bit stressed after.
But after overnight inside, they are recovered, and go out again.
If they don't fully recover, and still a bit peckish, I still put them outside---but in the shade if temps allow.
My situation is-----I started too early, and will have to put them in the ground a month earlier than planned.
Can still get frost till early June.
Ordered a "portable greenhouse" and bought a heater to extend the season, as 2' tall plants in 3.5" pots is a bit beyond design capability.
But, I have my overwinter plants inside a real glass and wood green house, with only a single heat lamp on a thermostat, and my remote sensor on the plot for the current season shows soil temps already in the 90's by noon.
The real greenhouse keeps the temp above 50 even when it's covered in snow (2 weeks ago) but the big plot with plastic greenhouse is an unknown.
I can still get a week or so of freezing temps before June.