I apologize if I'm nitpicking here, but isn't it the other way around? I always thought that a thinner wire makes for more resistance because there is less surface area for the current to move across and therefore requires more voltage to get the same amount of current to flow through it compared to a thicker wire, sort of like drawing liquid through a needle. The finer the needle, the tougher it is to pull liquid through it.
Ok to follow your analogy with a needle, yes a smaller needle will squirt a stronger stream that a larger gauge needle. So if you were to keep your Voltage and Resistance the same, a smaller gauge wire is going to have a higher current flow than a larger gauge wire. Now with that said there is one other thing that is a byproduct of resistance and current flow that is friction.
So rub your hands together slowly, they don't get hot. But rub them really fast and they do... same with the wire, the smaller gauge wire has a higher current flow so the resistance is going to generate more heat that with a larger gauge wire.