Heat is kinetic energy, its just randomized. It isn't the conversion of kinetic energy to heat that makes the mass change observable, its the subsequent dissipation of the heat that does so.
The difference in mass is observable only when the binding energy you release gets outside of the measurement apparatus. Because the mass-energy equivalence goes both ways, any instrument that is set up to measure the mass won't register a change until that heat also dissipates. This equivalence is why physicists will frequently clarify what they mean by distinguishing "rest mass" from "mass", where "rest mass" is the mass that the body will have once it comes to rest.
Thought experiment: A stretched ideal spring sits inside an isolated enclosure with an instrument set up to measure the mass of the spring, enclosure and everything inside of it. You release the spring and it vibrates back and forth indefinitely. The instrument registers no change in mass at all.
Variation: The spring is not ideal; it has some damping. The enclosure remains ideal. You release the spring and it vibrates back and forth a little bit before damping slows it down and releases some heat. The heat stays inside the perfect enclosure. The instrument still registers no change in mass at all.
Variation: The enclosure isn't ideal, either. You release the spring, it vibrates back and forth a little bit before damping slows it down and releases some heat. The heat escapes the imperfect enclosure. The instrument registers a small change in mass, proportional to the energy released / speed of light squared.
Yeah, I meant as in "some heat escapes into the environment". That makes a lot of sense, thanks for the explanations as this stuff can be quite unintuitive at times :)
