Here's the answer I got back:
The AIRS source code is ITAR controlled and is not cleared for public release. All AIRS Products are available from the GES/DISC. We also have direct broadcast software to allow local product generation. More information is available at: http://airs.jpl.nasa.gov/data_products/data_products_toc/"ITAR stands for "International Traffic in Arms Regulations". It covers exporting military weapons to foreign counties or to foreign individuals. The list of items it covers includes satellites and related equipment. The link in their response, by the way, points to various tools, but no source code for actually processing temperature information.
However, ITAR is related to the export of these items. And as I'm a U.S. citizen with no plans to export the code, it's not clear to me how this covers my situation. I sent a response to NASA saying as much and asking for their explanation of the matter. We'll see what they have to say.
Here are screen shots of the e-mails, with personal information blacked out.