I have a 2001 chevy S10 that on initial startup after sitting overnight it runs rough and the engine vibrates! after driving a few miles the symptoms disappear and it runs fine.
I suspect that it is a problem with coil packs or the spark plug wires getting moisture in them and dissipating when warmed up!
Trying to remember, does your S-10 a regular carburetor or throttle body fuel injection, if it has the latter, it should have a water temperature sending unit, some where on the top front of the motor, in the water manifold, it should have a plastic snap on cap with, if I remember wright it should have two wires coming out of it, it controls the fuel / air mixture, while the engine is cold, this sending unite might have gone bad, unplug it with a cold engine, while it is running, check to if there is any difference in the way the engine runs & try it again after the engine warms up, if there is no difference ether way I would say the send unit is bad. if sound like it might be something you don't wont to try to do, take your pick to a local auto part store, to see if they can test is, usually this is done for free, Thank you
2001 has OBD-2 system if your idle is rough ,is the check engine light "ON" if so have the codes read at the parts store. This will narrow the cause. FYI the computer in the truck doesn't control emissions until the water temp gets to 180 F . Also if the spark plugs or wires are the cause a random misfire code will be stored in the memory.
I had the same problem with my 91 S10 Blazer. After replacing several parts the engine stopped shaking like that after we put new O rings on the injector heads. I recommend getting a throttle body repair kit which includes all the gaskets and O rings.
All ready replaced throttle body & updated injectors, Co sensors, 2 vacuum lines on engine, and fuel pump & filter, and fuel & vacuum lines to rear of Blazer, and clean Ox Sensor, all no help
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