Hardening off minimum temperature

So I want to put my girls outside this week but the temp is about 55 F and overcast. Is this too cold to start hardening off for an hour, then 2, 3 etc..
Thanks

i only hardened my plants for 3 days and they did well. I put them in the window with a CFL on them. 6 hours first day, 10 hours the next 2 days. Plant on a cloudy day

Wish i could do that, my window ledges are too visible to neighbors, plus too many plants.