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It would probably do us all much good to go (re)read what Francis Sears has written in his text, An Introduction to Thermodynamics and .....I have the 1953 edition. Chapter 4, The First Law of Thermodynamics has some fairly strong statements about heat, work, and energy and the use of those terms. A few quotes (you should go read the whole chapter yourself):
NASA words (heat content) are bad. But thermal energy content is bad, too. Maybe they should say the internal energy of the oceans is increasing primarily due to heat flowing into it from the (warming) atmosphere.