Am I doing this too early?

Do they have a good heat lamp in there? If not, yes, it's way too early. If they have a good heat source, with a backup in case it goes out, they'll be fine. I put mine in the coop with two heat lamps at two to three weeks of age all the time.
 

I'd head outside and bring them in if there's no lamp. Or bring a lamp out to them. At two weeks the babies still need to be at least in the high-80s, temperature wise. You may find some cold-shocked chicks tomorrow morning if they stay out. 

My chicks went out into an outdoor brooder at seven weeks, without a lamp, and are doing fine. Once they have their feathers they can spend more time outside. I'd say five weeks at the earliest?

But if you give them a heat lamp they can be in the coop from day one. 

I have chicks out in the coop from 4-7 weeks old and they still have heat lamps for night. You did this way too early. They MUST have supplemental heat for another month or so at night and at two weeks old, even in the day.
 

spin off from the original posters question...

if you have a younger bird (2-3 wks) in a coop with at least 6 other older birds (6-8 wks) would you need a heat lamp as well? Or would they provide enough heat?

Quote:

Originally Posted by kmatt87 

spin off from the original posters question...

 

if you have a younger bird (2-3 wks) in a coop with at least 6 other older birds (6-8 wks) would you need a heat lamp as well? Or would they provide enough heat?

Yes they need supplemental heat.  The 6 -8 week olds are not going to mother the chicks like a broody hen.  Rule of thumb always...

Hatch - 1 week old               95 degrees required

1 wk - 2 wk                          90 degrees required

decrease temperature requirements by 5 degrees for every week of age after 2 weeks of age....so 85 degrees for 2-3 week olds,  80 degrees 3 -4 week olds and etcetera.  Those requirements are day and night.  Once they are fully feathered usually about 6 - 8 weeks for most birds, they need heat supplemented at temperatures below 50 - 60 degrees or overnight temps maintaining below 60.  They are babies.  Most will not approach their full grown sized until they are 8 - 10 months old....some continue growing well beyond that age; especially roosters.

The older ones will keep younger ones away from the warmest areas. Trust me on this. They will not snuggle with them, most likely, but harass the smaller ones. I have a group of 23 chicks, from 4-7 weeks old and the biggest ones hog the heat lamps and often keep the younger ones clumped in a corner away from the best and warmest places. Good thing they're all fully feathered at this point and at times, the older ones actually roost, leaving the smaller ones room under the heat lamps at night.
 

A heat lamp is not that expensive, but a regular light bulb will put off some heat, just maybe not enough for 2 week old chicks. You never said how large the coop is.
 

The brooder hood for the lamp with a porcelain base is about $10 and the 125 watt white heat bulb is about $5 around where I live. It doesn't cost much to run, no more than a regular 100 watt light bulb.

Pardon me for saying so, but it doesn't seem like you did any research or planned much at all for this. A storage box? You didn't do it right at the start, but you can change it now. You have to do right by the animals you now have in your care. Chilling at an early age can cause issues later on. Get yourself a copy of Storey's Guide to Raising Chickens or Raising Chickens for Dummies (co-written by our own Nifty-Chicken) and learn what you didn't learn before you got them.