You really want to transplant seeds into your medium of choice when the taproot is just barely protruding out of the shell. If it comes too far out, it's common to stunt them by damaging the micro roots by peeling it away from the paper towel and/or roughly placing it in the soil.

Don't let the medium dry out, and hopefully they'll make a turnaround. Also, I once tried germinating some seeds on a piece of equipment that gets a little too warm, and ended up having one of the seedlings sprout itself entirely out of the shell and into the paper towel. This is definitely undesirable, and I can't give any advice on survivability because I just threw that sprout away on account of its poor demeanor. If you went ahead and planted them anyway, just make sure the soil is doesn't dry out completely. Underwatering seedlings is usually a death sentence because the seedling doesn't hold enough moisture to sustain long droughts. But overwatering can lead to poor growth and damping off, so you just have to be watchful during the early stages.

Next time, if you plan on using paper towels to germinate, keep the seedlings in a dark spot that's slightly warm (NOT hot) to the touch. I use paper towels most of the time, and I actually don't even bother leaving them in a warm spot anymore. I just keep them in a ziplock baggy inside a drawer in my nightstand. I get the same germination method that way as I do keeping them on a warm appliance.