I have same issue on MY Ď91 500SL.
My strategy will be: -
1) engine warmed up. Ignition off. unplug coolant sensor and jump plug with 2no. 470ohm resistors diagonally across socket. Start engine. Does temp gauge come back to life?
Yes? Suspect defective sender unit. Check resistance diagonally across pins of sender. Resistance should be roughly 250-450 ohms.
If gauge doesnít come back to life when you jump socket with resistors and restart engine, go to next.
2) Remove cluster. Unplug cables. Examine. Reconnect. Does this solve problem? No?. Next.
3) Remove front glass bezel. 3 screws. Remove mpg/oil/coolant temp gauge. Pulls straight out. Examine long square profile pins on back of gauge, and corresponding sockets on circuit board. Clean pins with emery paper. Tease sockets with small screw driver so as to make better contact. Refit gauge. Donít refit bezel at this stage. Just reconnect plugs at back of cluster. Restart engine. Problem cured? No? Next.
4) purchase gauge or complete cluster from junkyard. Make sure you get a compatible gauge or cluster. I.e. pre Ď93 in your case. The motors for the gauges inside later clusters have round pins on back, not square. Round wonít fit in square holes. Get compatible gauge and swap over defective combination gauge.
Now, hereís where it can get a bit tricky. Depending on the mileage of the parts car, you might find that the temp and oil gauges work, but the mpg gauge is erratic or doesnít work as good as your old one did. You can swap over the motors, but you need to be 7/10 in DIY skills. It involves removing the gauge needles. Note where the needles sit in rest position. Some rest against a small black pin. To get needles back in correct positions when you eventually put all back together, it is best first to remove these pins before removing needles. The needle will then fall back to its natural rest position. Take photo of this. To remove pins, fold piece of paper/kitchen towel over pin. With small pliers, pull pin straight out. Do not twist or lever. Then remove needles with two small spoons under central boss as a lever. To avoid marking the black face of the dial put sheet of paper under spoons. Once needles removed, grasp tab of black dial face and very carefully lift. Itís sticky and will come off relatively easily without bending or marking the black face. Place dial face to side in clean area. Small screws. Remove and withdraw motor. Swap motors. Rebuild is reverse sequence. Refit needles according to photo you took earlier. Then pins.
Early clusters and gauges are becoming harder to find at junkyards. So if you are only able to source later one with round pins, you can cut the pins off the back of the motors and solder on your old pins on to rear. DIY skills needed? Maybe 8/10. Up to you.
Alternatively you can buy a whole new cluster from MB