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// Removed as I'm not a physicist and may be mistaken.

I think it's correct. Heat is the flow of thermal energy. A portion of that flowing energy is converted to electrical energy. Perhaps you're confusing heat with thermal energy?

There must be some heat flowing to generate electrical power because of the 1st law, so even if the effect is described as being due to a temperature difference, in practice, you also need a heat flow to be useful.

Your quote about "without any side effect" means without heating up a cold reservoir. But the article doesn't claim that.

Heat is the energy, not the flow. That flow is flux or power. A temperature difference is how we perceive or measure a difference in thermal energy density between two places, and is the potential that drives heat flux. A thermoelectric barrier between those two wells can extract energy from that flow, within thermodynamic limits.

Yes, I was a bit sloppy. It's the flowing energy, not the flow of energy. The point of my comment was to distinguish heat from stored thermal energy so the distinction isn't so important in that context.

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