The Dorsey Brothers are generally remembered for leading swing bands that leaned towards sweet and away from hot. It's difficult to deny the jazz authenticity of their earlier playing though, on what must be hundreds of records. Again and again they prove their worth.
Sure, there are weaknesses - Jimmy tends towards a certain formulaic approach, and I'm always slightly worried he'll lose coherence (as he does on the Trumbauer/Bix record of Singin' the Blues). Tommy is probably more consistent, but perhaps more derivative as well.
On Hot Heels, they are in on a little conspiracy to dupe the listener. Pay close attention to the trumpet solo (by Tommy Dorsey, always more rhythmic and hot on that instrument than his usual trombone) - the very highest notes are actually played by Jimmy on clarinet.
Here's a great record featuring Tommy on trumpet once again. What a stomping sound they achieve here! It turns out white jazz bands in the 1920s were not necessarily corny or polite...