You can do a quick an easy test by feeling the hoses during and after its warmed up (be careful as the hoses my be very hot). Let it run just sitting in driveway or garage. As its warming up run your hand along the hoses feeling for any temp changes between the upper and lower Rad hoses. Then the same along both heater hoses. Continue doing this until the engines at full operating temp. The Rad hoses should both feel hot only after its warmed up and the thermostat opens. The heater core lines should warm up much faster. If any feel considerably cooler than the other then there maybe something wrong with the thermostat, hot water valve, or the heater core.
To flush the core you'll need to remove both hoses at the firewall. Install some temporary hoses, long enough to go over the fender. Connect a flush tee on the one that would normally be the return line from the core. Connect a garden hose to the tee. Turn on the water about half way. Now place your thumb over the open end of the tee to modulate the pressure and see if water and any gunk come out the other hose. DO NOT PUT FULL WATER PRESSURE ON THE CORE AS IT MAY RUPTURE!
2001 Ranger Edge 3.0 V6, 5 speed M/T
Limited Slip Differential, James Duff Traction Bars
Kumho 30x9.50 15 MT / Black 297 Series 15x7 Rims