Unless it's changed in the last few years, Car Talk is recorded Wednesdays from about 10am to 1pm (give or take, but it's usually three hours) in the studios of WBUR in Boston. Callers to the 888-CARTALK number at any time of the week get a voicemail greeting telling them what info to leave...name, question, number to be reached at on Wednesdays, etc etc etc. Then the producers call them back while recording, and it is true that the producers don't give Tom and Ray any warning about who each caller is or what their question is...they like to see Tom & Ray squirm. ;D
Anyways, the CT producers then take the Protools session back to their offices of "Dewey Cheatum and Howe" (yes, a real company - it's the parent company for CT and all their commercial ventures, too) in Haaaahhvaaahd Square and edit it down to a 59 minute show each week. It gets distributed via the PRSS ContentDepot satellite system Friday nights.
Most stations air CT at 10am Saturdays because it's a prime time for listening and it's a very popular show (with strong earning potential). They start with Weekend Edition from 8am to 10am, then Car Talk 10am to 11am, and then either Wait Wait Don't Tell Me or Whad'ya Know. After 12n the prime time window mostly closes and listenership tends to drop off.