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In order to obtain a temporary hunting permit, you would need to get a temporary import permit from the Secretariat of National Defense prior to traveling to Mexico.
Here is their phone number: 52 55 2122 8800.
Here is the website as well: http://www.gob.mx/sedena
There is a special permit available for the transportation of firearms for hunting. You should contact a Mexican lawyer though who can help you with the application process unless you are fluent in Spanish. Hiring a Mexican lawyer would be easiest anyways since documents will need to be filed in Mexico.