thats a hard one.
but the temp. don't go up.
ten minutes and the engine is not hot at 50d f ambient?
you have 2 problems. not 1.
maybe 3
1st any tune ups in the last 100k miles. (30kand 60k are manditory)
can you keep car idling by playing with right foot on gas pedal.
get car good had hot , then grap top rad hose ,if too hot to hold hand on hose then car is good. if it is not hot, 180F is hot. (70 degrees more than a HOT TU

then your thermostat is bad, or wrong one ,ormissing or missing the special gasket used on all kicks with deep socket thermostat pocket.
you could have a leaking injector.
1 tune up
2 stat, check temperature with an IR gun. get hard data.
3: ECU in limp home,
Is CEL lamp on ,keyon no start,then out after starting.
?????