Tomato Seeds

I haven't had very good luck with these. I started them 2+ weeks ago and nothing has come up. These are seeds from a seed catalog that I know are good so I figure it's a problem with me not the seeds. I had tried some seeds from Wal-Mart over a month ago and they sprouted after 3 weeks but have failed to live.

A few days ago I tried taking some of the seeds out of the pots, it's really hard to find tomato seeds in potting soil, and I put them on a wet paper towel in a bag in front of the wood stove. It worked! After only 2 days I have 6 seeds that have sprouted. Now the dilemma, what do I do with the little pots I put them in? Everything I have read says they should be set under a fluorescent light. I wonder if that's really necessary. The weather here is supposed to be sunny and in the 80s for the next week, can I just put them outside during the day?

I really want these to make it so if anyone has any suggestions I could really use them.