Mitsubishi: no heat in a 2003 mitubitzi galant, galant, heater core

Question
I changed the thermostat.  I filled the radiator. still no heat. the top and bottom heater hoses are hot but the smaller hoses going to the heater core are cold. the blower and heater work blows out cold air.  Where is the heater control valve

Answer
I take it that your temperature gauge is working properly.  That means that the temp. sending unit is also working.  With the thermostat replaced as well... it leaves us at this point: I believe that you may have a blockage in the hoses to/from or heater core itself.  If possible, you should try to disconnect both of those small heater hoses on the firewall, and try to flush out the heater hose with a water hose.  Any household hose from the house with reasonably good pressure will work and it shouldn't take much.  If you can't unclog the heater core then it would have to be replaced.  Replacing the heater core is a bit more work.  Other than that the heater/temperature control valve is directly hooked to the Hot/cold red/blue temperature adjustment on the dash control.  It moves a flap open or closed to force air through the heater core for heat or bypass it for cool air.  If the cable became dislodged/unhooked/jammed it would no longer open or close the valve and only blow cold air.   But... since you said that the hoses to and from the heater core were cold... you don't have a hot heater core... and thus no heat.  So start with that heater core!  Good luck!