Start with the simple things, clean the radiator, you might have to remove the hyd oil cooler to get it clean. Even if it looks like it is clean a good scrubbing usually makes quite a difference. With these older machines you get oil leaks, then you get oil on the radiator, then dirt sticks to it and then it's overheating. Most of the cooling systems on these machines were barely able to keep them cool in good conditions so it doesn't take much dirt to get them to overheat.
Regarding the final drives being a weak point, it is mostly just the design. A lot of this generation of excavators had final drives with shafts and bearings that are just a little too small or weak for the job. They can barely take the stress of normal working conditions, put them in any hard work or slight abuse and they break. They are not like the planetary drives on modern machines, just keep some oil in them and they can take just about anything you can throw at them.
