Without Water Temperature Sensor

WARNING: This page is about a different car, the 2014 Mazda 6. However, it is still accessible from the selected car via links, so may be relevant.

Remove the battery. (See BATTERY REMOVAL/INSTALLATION [SKYACTIV-G 2.5] .)
Drain the engine coolant. (See ENGINE COOLANT REPLACEMENT [SKYACTIV-G 2.5] .)
Remove the insulator.

Fig 1: Identifying Insulator With Nuts
Courtesy of MAZDA MOTORS CORP.
Remove the clips and remove the heater hose.

Fig 2: Identifying Heater Hose
Courtesy of MAZDA MOTORS CORP.

Fig 3: Identifying Heater Hose Clip
Courtesy of MAZDA MOTORS CORP.

Fig 4: Removing Heater Hose
Courtesy of MAZDA MOTORS CORP.
Install in the reverse order of the removal.
Inspect for engine coolant leakage. (See ENGINE COOLANT LEAKAGE INSPECTION [SKYACTIV-G 2.5] .)