I've often speculated (though certainly not concluded) that it was more of a widespread manipulation of mind and sensory perception than true heat. While not unlike that of the Talosian's abilities, it would be far in advance given the Organian's true evolutionary nature as pure energy beings. Regardless, If I recall correctly, they still had to concentrate their efforts to accomplish the task.
It does make more sense for it to be that way as opposed to physically heating all of those weapons consoles, phasers, disruptors, etc. throughout the Federation and Klingon forces combined. Still, though, it was a truly amazing thing for them to be able to manipulate that many individual minds, not to mention the vast distances away most of those minds were. Even if it took all of their combined efforts to get the job done, I don't know of any other advanced race in ST that powerful, with the possible exception of the Q Continuum.