ummmm my book sez its the other way around... wire with the same resistance but of different dia will result in the thinner wire heating faster than the thicker wire.
and if you have 3ish" of lets say 30 gauge and 2ish" of 24 gauge ( both having the same resistance in a coil form ) the 30 ga coil will heat up quicker, since the thicker wire has more mass and dia, electron flow is dispersed across a broader face thus decreasing the "electron friction" ( which causes the heating)