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> A few weeks later, I even started receiving political flyers in the mail. I guess you can just buy a voter registration database for this purpose, and it includes temporary addresses.

This is (mostly) public information. The Secretary of State in most cases makes this available in some form or another for raw consumption but the preferred method is to buy a cleaned and collated version of the national voter file from one of the vendors. Usually this is also joined to a consumer file which includes additional demographic and contact data.

In California, that would be PDI who also offers a CRM for voter contact. Nationwide, from the Democratic side of things, you're looking at Targetsmart or Catalist - unless you're a campaign or other hard side organization receiving access via the state or national party. On the Republican side it'd be the Data Trust. There are "non-partisan" third party voter file vendors out there too but the data isn't as reliable as the partisan options.