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The ash itself should not damage the car any further. I would certainly sweep away any ash under the front air-intake area. Once outside you will be able to measure any damage. Take pictures for any possible insurance related items. Give car a good wash and detail. See if the inside has any smoke damage or smells.

I would also suggest being careful around the area the Battery Tender was plugged in. Make sure no fire damage got into that area or wires. The Fire Department should have done a good assessment. Follow their precautions.