Carburetor? What's that?...I'm no help, all my HE is diesel-powered.

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Never a dull moment at Berry Hill Farm.

I don't suppose this is something that could be faked?

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"It's normal for these things to empty your wallet and break your heart in the process."
2012 SLK 350
1987 420 SEL

Gasoline scares me...it's so inflammable!!!! You could be burned.

Seriously, the prior posters seem to have hit the nail on the head, diagnosis-wise.

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Never a dull moment at Berry Hill Farm.

Andrew,
You do not have an alternator; the K series Kohlers used a Delco Starter/Generator. This is a DC geberator which can also function as an electric motor, hence the term Starter/Generator.
It should NOT get that hot. You need the check the wiring, regulator and the S/G itself. I have a link to a small tractor S/G diagnostic site, but its not here. I'll try to post it tomorrow.
Where are you located?

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1982 300SD " Wotan" ..On the road as of Jan 8, 2007 with Historic Tags

The link for the Starter Generator discussion/diagnostic is here:
www.simpletractors.com/service/electrics/starter-generator.htm

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1982 300SD " Wotan" ..On the road as of Jan 8, 2007 with Historic Tags