There will be, based on the mass of the metal. Thicker wire (22ga) is lower resistance, so to bring it up to the same resistance as the thinner wire (28ga), it'll take a lot more wraps, so the wire is thicker, and there's a lot more of it, so the 22ga is going to take a lot longer to ramp up. Unless you pound it with massive wattage.
Andria
With the resistance letting the same amount of current through, that's where I get confused. Then again, it makes sense that the thicker wire is going to take longer.