Do you have lights hanging over your dryer? The most important thing is to have them directly under lights, 2-3" from the bulbs. They can do without the bottom heat (assuming that thats why they are on the dryer)

No Lights :\ Just a window directly behind the dryer.

I took some of the sprouted seedlings out of the trayes and put them directly by the windowsill (pics below)

Do you think these tomato seedlings are leggy? What else should I do to these at this point?

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Yes, unfortunately they are leggy. They always will be with only window light as there simply is no way it can provide either the intensity or the hours of light they need. The only way to prevent leggy seedings is with supplemental lighting. There is a FAQ here and lots of discussions about it.

If you can't provide it then you will need to transplant the seedlings frequestly, deeper each time to bury all the stem, until they are ready to go into the garden.

As to bottom heat, if they are on a source that only runs intermittently then remove them when the fryer is running. If they are on a heat mat then they need to come off it as soon as the first few germinate.

Dave

Here is a link that might be useful: FAQ - Growing from Seed