they will need to be 'hardened off' first. .... you cant just throw indoor grown plants outdoors and hope they live... the sun .. which is where sunflowers go .. is much too strong compared to artificial light or thru a window pane ...

and they should not go outside until all danger of frost is past.. i don't know that date for your zone ... call any local garden shop or nursery for such ... even if that day is today .. they will still need to be 'hardened off' ....

good luck.. ken

I am in zone 7 NC and our last estimated frost is April 15th, but this may not be accurate for your area. In my zone 7, I would not plant Sunflowers outdoors until after April 15th unless I was willing to start over and had plenty of seed to spare just in case. A lot depends on how close to the coast you are, which would set back the date a bit more. I have found that Sunflowers dont do well in pots. I have also found that they can be raised at different times during the growing year. Sowing some early, mid-season, and some later will give you Sunflowers thru the entire Summer until frost. Try going to your local region's forum to ask the same Q. Local advice is always the best. Happy growing!

Here is a link that might be useful: zone map

I second quirkpod's suggestion of checking for a regional forum; or if you have a local Extension agent, give 'em a call. They'll be glad to help you out!