My car has hard starting and if it starts it iddles at a normal idling bt suddenly it rise up its reves and cut off with black smoke at the exhaust. what might be the problem? thanks in advance

I do believe you are correct, but here's how the system works. You turn the switch on, the computer is activated, the temperature sending unit, sensor sends a signal to the computer that it's cold so the computer sends out a signal to the engine to go into cold start mode. The fuel is enriched into the cylinders by raisin the idle just a bit placing more fuel into each cylinder, and the idle is advanced by a little electric plunger at the throttle body. Once the engine has warmed, the water temperature sensor sends a message to the computer to take the engine out of cold start mode and into normal run. Now you can understand why the temperature sending unit/sensor is so vital to proper starting procedure. Replace the temp sending unit/sensor and she will work just fine. School's out. Time to go to work.

Blue smoke is not good!! Piston rings are bad or valves. On a Mercedes it will cost you more than the car is worth at this point. Unless you have a sentimental attachment to the car and really really want to keep it., I would get rid of it. 123,000 mile is a great life for a 1989.

Black smoke means rich mix (gas, not diesel right?). Bad coolant temp sensor?

this car must be a Diesel as this sounds of a injector pump failure , there are two fine machined plates with groves cut in them "inside pump" after a lot of miles these two machined plates are not so machined anymore and fuel slips by causing the symptoms your describing , pump will need to be rebuilt and flow bench set or replaced with allready rebuilt/set unit to get things back to normal

run fault codes and check for MAF/MAP sensors and HO2S and HO2 sensors.

Check the fuel pressure regulator. It may be bad. Pull off the vacuum hose to it and check for any sign of gas in the hose. A busted diaphragm in the regulator could let extra gas into the intake through the vacuum hose. The black smoke indicates it is getting too much gas-running rich.

Turbo is bad, when you start seeing black exhaust turbo has gone out completely. Depending on how old the turbo is and how hard it is driven, how many miles and so forth.

When an engine expels black smoke it means that the piston rings are going and is consuming oil. And when the color of smoke is white the engine is consuming more fuel. Both are harmful. Black to the engine and pocket while white to the pocket. It seems that the injector need careful attention.
Cold engine does expel white smoke initially. When the temperature rises to normal working temperature the smoke stops. This is normal in your case. 5 to 10 minutes to warm up is normal for any diesel engine. But any thing more than that needs attention.

did you check for vacuum leaks probably a vacuum hose thats been knocked off or eroded and needs to be replaced.

Hi , I`m not sure about the 01 model but the 98 model got this roker cover gasket problem because it`s too close to the exhaust and with time can`t handle the heat.So when you rev the car , dropping oil on to the exhaust and one little drop of oil can make big smoke which coming up around the turbo. Hope this helps .