I have a 1998 Legacy GT with 2.5L.

i would check your waterpump and if that dont fix it its a blown headgasket

yes, the water pump is what circulates your coolant.

Water pumps on the 2.5i have always been VERY robust. Before digging in there I would remove and blow out the heater hoses, as they're inline with the system. Folks who've added a stop-leak product to the radiator in the past can experience blocked heater hoses (under the windshield, by the way). If the WP's pulley fell off the motor wouldn't run. If you've replaced the t-stat (which are super-robust, with a large orifice), ensure that it was indeed one with the OEM large orifice. A blown head gasket will NOT interfere with coolant flow, by the way. You'll have bigger fish to fry! Be sure you're checking for flow once the motor's warmed up, of course. RSVP Ern

The thermostat allows the water to circulate thru the radiator when the block water temperature reaches the specified temp. . Does your temp gauge go up to the normal operating temp.? Does it go up past normal operating temp.? Are you sure you put the thermostat in in the correct direction ?(The bigger end goes in towards the block.) Now we can talk about the water pump, is the belt tight on the pully ? Can you spin the water pump pully without the belt on it , does it wobble side to side? Pull the t stat and leave it out fill the coolant run the engine with the cap off and see if you have flow , with nothing restricting the flow it should have flow . Now that you have done all the simple stuff first and it is still a problem check the t stat to be sure it is the correct temp for your car. Still a problem then do a cylinder leak down test to find the problem like david suggested.