Hey, I'm new to this forum, but I'd like to try and answer. Sound is the propagation of waves of physical pressure and force. Ultrasound is those waves above 20 killahertz in frequency, which can not be commonly heard.
Heat is a term I really wish would be removed from common physics vocab because it can many different actual physical phenomena. In many ways heat is the same physical thing as EMF, or light. In our common speech however "heat" actually refers to "infrared" light, which is lower in frequency than visible light.
So can the propagation of pressure waves create EMF? Certainly, how much and of what kind depends on the frequency of the pressure waves, and the material (and said materials natural frequency) through which it is moving. Sound acts differently in different materials so it's hard to say without any of that information. I don't know of any equation where you can punch in a sound wave frequency, a material natural frequency, and get out interference results.
You may be thinking of water cavitation where ultrasound is used to produce bubbles of steam within water. I've heard when these tiny bubbles collapse the water inside can reach around 5000 degrees. Here's a video (you may want to turn down your sound), displaying the production of cavitation via ultrasound in water, . I couldn't find any equation of the relationship between the sound and the heat of the cavitation produced for you though.