Is this a valid explanation of why hotter things have more mass?

[Evanish]

Is this a valid explanation of why adding heat also adds mass?

The closer to the speed of light something is going the more force it takes to increase it's acceleration in that direction. If you have two objects of uniform composition and if the only difference between the two is that one object is hotter then the other then the hotter object will have its atoms moving more quickly. Whatever direction you push the objects the hotter object will have atoms moving in that direction closer to the speed of light therefore it would take more force to increase its acceleration therefore it has more mass.

 

[Evanish]

I meant why hotter objects of identical composition have more mass. I can't figure out how to edit the title.

 

[mfb]

The closer to the speed of light something is going the more force it takes to increase it's acceleration in that direction.

Even keeping that acceleration needs more and more force.

If you have two objects of uniform composition and if the only difference between the two is that one object is hotter then the other then the hotter object will have its atoms moving more quickly. Whatever direction you push the objects the hotter object will have atoms moving in that direction closer to the speed of light therefore it would take more force to increase its acceleration therefore it has more mass.

Some of them will do, but other atoms move in the opposite direction, so you need less force for them.
There is a tiny net effect - a hotter object has more energy, and therefore more mass. But this effect is really tiny. The mass of boiling water is larger by 22 parts in a trillion compared to the same amount of water at the freezing point.