How do I blank out the mac screen when I am viewing an external monitor?

Aattach an external keyboard and pointing device, AND connect the power adapter. THEN close the lid.

Use your Mac notebook computer in closed-display mode with an external display - Apple Support

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Batteries DO occasionally go bad and swell, but it is Not caused by heating during use. It can be caused by storage at excessive temperatures, such as in a hot closed car in the sun.

Heat buildup is NOT an issue. You Mac measures many internal temperatures multiple times a second, and adjusts the fan speeds until they are running at speeds needed to unload that heat.

You paid dearly for that built-in display, The Mac is ready for you to continue to use it, by concatenating both displays along any edge of your choice into one larger "Extended Desktop":

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close the lid