by 91_2600i over a year ago
There is an idle air control valve on the top of the throttle that regulates idle air - as it warms up, it allows less air to "Bypass" the throttle. In fact, Mazda calls it a Bypass valve. Yours is probably stuck wide open. They get gummed up over the years and will tend to stick.
You can test each of the those two parts, but even if each tests OK doesn't guarantee that they're are not faulty.
IAC Valve:
Disconnect ISC valve electrical connector. Connect ohmmeter to ISC valve 2-wire connector. Measure resistance. See ISC RESISTANCE SPECIFICATIONS table. If resistance is not within specification, replace ISC valve.
http://static.mazdabscene.com/photos/2015/220/93122/l.jpg
end quote