Temporary Importation Permits for cars

Yes, the procedure must be started in one's home country. It is necessary to show the financial ability to live in Mexico without the government's support, and this part of the process must be completed in the your home country.

Then, when you enter Mexico, you have to get a special temporary visa upon entry saying that you will be exchanging (the Spanish word is canjear) the visa you received in the U.S. or whatever for the real deal, which is the Temporary Resident card. This final exchange (canje) has to be done in Mexico.

Beware! Don't just get the usual tourist card when you enter Mexico, or they'll reject it when you apply for Temporary Residency (as I found out by bitter experience). I'm having to repeat the process in December.

The people in imigración are sticklers for detail, IMO.