Then you'd better check again. As benit13 said nothing changes the rest mass of a particle. It is the mass of a particle with no regard to motion. Now, when you heat something up then the particle's kinetic energy increases and the particles gain momentum. The total energy of the particle then obeys \(\displaystyle E^2 = (pc)^2 + (mc^2)^2\), where we are using whatever average p is appropriate. But m is the rest mass and does not change under any circumstances, even when changing reference frames. Now, if we are talking about a macroscopic object its rest mass due to the individual particles stays the same, so we still get the same rest mass. What happens is the mass of the whole object reflects the extra kinetic energy contained in it. This does change the mass of the object, but not it's rest mass. The thermal energy simply gets absorbed into its total energy.

-Dan

It's not that I want to undermine your authority or something, but I've made some google search and those are some of the results:

According to the $E=mc^2$ equation, will an object whose thermal energy (temperature) rises also weigh more? And by the same token, will the mass of an object decrease as its temperature approaches...

physics.stackexchange.com

From special relativity theorie we know that $E = mc^2$. When a system acquires energy, mass becomes greater. That is clear for kinetic energy, because we have a formula that gives m as a function...

physics.stackexchange.com

This book mainly focuses on the theoretical and experimental study of non-Fourier heat conduction behavior. A novel thermomass theory is used as the theoretical basis, which provides a general heat conduction equation for the accurate prediction of non-Fourier heat conduction. In order to prove...

books.google.pl

Does mass change with temperature? - Quora
Generally, opinions are pretty divided among physicists, however it seems, that according to the majority, heat transfer DOES indeed increase the rest mass of a macroscopic body - although this increase is very tiny. Here's also a site, which proves that the increase of electric charge is resulting in small addition of rest mass to the system:

Compute total energy of a relativistic object. Compute the kinetic energy of a relativistic object. Describe rest energy, and explain how it can be con

openstax.org

*"Both the actual increase in mass and the percent increase are very small, since energy is divided by c2size 12{c rSup { size 8{2} } } {}, a very large number. We would have to be able to measure the mass of the battery to a precision of a billionth of a percent, or 1 part in 1011, to notice this increase. It is no wonder that the mass variation is not readily observed. In fact, this change in mass is so small that we may question how you could verify it is real. The answer is found in nuclear processes in which the percentage of mass destroyed is large enough to be measured. The mass of the fuel of a nuclear reactor, for example, is measurably smaller when its energy has been used. In that case, stored energy has been released (converted mostly to heat and electricity) and the rest mass has decreased. This is also the case when you use the energy stored in a battery, except that the stored energy is much greater in nuclear processes, making the change in mass measurable in practice as well as in theory."*
I would agree with your statements, if instead of

*"What happens is the mass of the whole object reflects the extra kinetic energy contained in it."*, you would say:

*"...whole object *__radiates out__ the extra kinetic energy contained in it.". I might be an amateur, but I know enough about mass/energy equivalence, to say that if:

*"The thermal energy simply gets absorbed into its total energy."*, it will actually result with a tiny increase of rest mass - but we won't measure it, since the additional mass/energy is immidiately released into the environment, due to the constant thermal radiation...

If we'll move on higher level in scale dimension, we will be able to use the same mechanism, to explain a scenario, where we hit a solid block of granite with a steel pipe, causing the increase of internal vibrations in both systems, which result in emission of a sound wave (among other waves) to the environment - so that in the end, the balance of energy emission/absorption is being maintained...

However, what matters at most for the discussion about fractal gravity and gravitational expulsion, is the ratio of energy emission/absorption. If an external source causes a constant increase of energy level in a body (or system of bodies), it's excess will be emitted into the environment, disrupting the initial balance of mass/energy equivalence. It's quite logical to me, that the additional mass/energy will in such case turn into radiation, that will influence the potential energy of another body by inducing a kinetic force on it or increasing it's level of thermal energy.

Here are examples of forces (thermal radiation, kinetic pressure of light), which are induced on matter due to emission of additional energy from a system:

And here's just another example of the same process - only here, it's the source of radiation, which is experiencing kinetic force of lift due to the potential energy of a body with greater mass (Earth):

All examples are based on the same laws of mass/energy equivalence. However, mechanical compression of a mass/energy distribution requires a different explanation - I will try to explain it better in another post...