Possibility you blew a head gasket when it overheated, if it gets really hot very fast when you give it some stick be prepared to shell out a couple of grand for a head job, it could also be a stuffed thermostat, blocked radiator or an air lock in the system but every WRX motor I've had has always run at a normal temp no matter what the weather or conditions are like, take it to one of the Sube workshops and have it checked out.

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Beaten up old 98 Gen 2 Liberty, 13.0, stock V3 STI running gear.
07 Transit motor home
69 VF & 70 VG Valiants needing full restoration
Yamaha Zooma 50cc rocket hopefully going with the Transit.