I had a Nissan about 20 years ago that always stayed on hot. Here's what I found:
The electrical connector to the temp sensor (usually near the thermostat) was corroded. With Nissan, no voltage passing reads "Hot". Perhaps with Subaru, no voltage reads "Cold". Take off the connector and clean it with sandpaper and contact cleaner and see if that makes a difference. Clean both the male and female connectors. Only takes a few minutes.
Hope this helps.
.
The electrical connector to the temp sensor (usually near the thermostat) was corroded. With Nissan, no voltage passing reads "Hot". Perhaps with Subaru, no voltage reads "Cold". Take off the connector and clean it with sandpaper and contact cleaner and see if that makes a difference. Clean both the male and female connectors. Only takes a few minutes.
Hope this helps.
.