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This is a poorly stated question.

What do you mean by size? Volume or mass?

By your question, if all other factors are constant, increasing the size, (whatever you mean by that) will have no effect.

If you mean that you have a mass at a certain temperature and you double the mass at that temperature, then the total energy doubles.

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Q: How will increasing the size of an object affect its thermal energy?
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Can you add thermal energy to an object without increasing its temperature?

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