Which seedlings need heat?

I have a heated propagator and grow light.  I am planning to a start onions, leeks, tomatoes and chillies under them.

I am planning to start them all with heat under the grow light.  But do I then take the onion and leek out once they've sprouted?  I know they don't need heat.  Do they go somewhere cold, with as much light as possible?

And broad beans, any point starting them with  heat and light?

Many thanks.