Tulip bulbs are splitters. Different than babies. And the small splits have to grow large enough to bloom. End of my knowledge. I leave them in the ground and any large enough do bloom the following season.

Have your splits produced foliage? A grow light only works for plants with foliage. Tulips are a cool season bulb. Why the heating pad? Did someone recommend it?

There is no foliage on the bulbs due to them lacking any roots. They were in a container however most of the bulbs ended up rotting and I saved what I could. I thought that since they don't have any roots, that a heating pad could help speed it up. I live in Canada, zone 5, due to it getting colder I brought them inside.

I figured it would take a few years before they actually flower, but I am glad that they will eventually regrow their roots. Should I continue to have them placed on a heating pad?

No. Heat now interfers with with their natural development and can force the bulbs into too early growth. Just treat them as you would newly purchased bulbs - plant in the ground or in a container. And be patient in your wait for flowers :-)

Agree with everythng Gardengal has said.

Wanted to add that very few tulip divisions "perrenialize" in the garden. If you have freezing winter temps. the Darwins (division 4) may return reliably in your zone.

Lucky you!