Yes that test will work, but if you intend to go through the trouble of
taking the t-stat out, why not just put in a new one?  Cheap insurance!
If the heater hoses are hot, once the engine is warm, maybe the blend
door not functioning and/or the core is leaking/clogged.  The hinges on
those doors have the nasty habit of breaking.  Your truck is 10+ yrs
old.  The lifespan of the core is right around 10yrs.  Check the
operation of the blend-door actuator.  If it is cable operated, unhook
the cable and manually turn the lever....the only sound you should hear
is a quiet 'thump' when the door closes off the heater core part of the
plenum. The better way to tell is to remove the heater-core cover in the
plenum and check the door for proper operation.....with that cover off
you can also tell if the core is a leaker too.  A new core and t-stat is
under $50.  Once they are replaced you are good for another 10yrs or so!

Hope this helps some.....

Dave S(Texas)