So, for a plausible idea.

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Heated pet blanket

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https://www.amazon.com/Homello-Waterproof-Electric-Adjustable-Resistant/dp/B07JGP75ZX/ref=

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Draws 50 watts on HIGH. 28 watts on LOW

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600wh battery pack $300

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https://www.amazon.com/Portable-Station-Generator-Outlets-Emergency/dp/B09HHFFL7L/?_

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So, running on high, full time gets you 12 hours. Put the mat in the lizard's cage.