i just looked at the abnormal checklist of our cheyenne III.
it is splitted there :
when the low oil pressure warning comes on and all other parameters ( ITT, Oil Temp etc) are normal it calls for reducing power as soon as practicable and land as soon as possible and be prepared for a sudden engine failure
when oil temps and ITT is simultany rising it calls for shut down the engine immedietaly and continue with single engine procedures.
on a twin or more engine i think i would shut it down even when it seems to respond when i do not need it at the moment and i can stabilize the plane single engine.
keep on running may result in a catastrophic engine burst / prop shaft failure, engine fire etc etc some time later and then you have a more worse problem.
in a single engine plane i surely would let it run until it carries at least its own weight when there is not a possibility for an immediate landing.