Mitsubishi Repair: 1991 Mitsubishi Galant Transmission/Overdrive Problem, mitsubishi galant, worst case scenario

Question
I own a 1991 Mitsubishi Galant LS 2.0 SOHC with 113,000 miles and have been having some transmission problems while it's in overdrive.  
When I first start the car up, it won't shift into 3rd gear.  About 5-10 minutes later when the car heats up, it goes into 3rd gear (25-30 mph) and goes fine on the flat but slips when going up a slight grade or hill.  I changed the transmission fluid and added Lucas and it's still not functioning properly.  It seems lke when the weather is warmer, it seems to run a little better up hills while in overdrive.  Once it's in gear it never kicks out and the other gears shift well.  I've been driving with my overdrive off and only driving with my first 2 gears.  I can hit 35-45 without overdive, but with higher rpms.  Thank You very much for reading this and God Bless.  Have a great day!

Answer
Dom,
You'll want to have your car's main computer module and transmission computer module inspected to make sure they are working properly.  There is a known issue with Mitsubishi using under-rated capacitors in their early 90's cars, which prematurely wore out and caused these problems.  

You should also have your timing checked and consider getting a full tune-up.  If your timing is off, your car will tend to hesitiate, stumble, idle poorly and not reach max speeds in all gears.  A tune-up should include replacing spark plugs, plug wires, distributor cap, rotor, PCV valve, air filte, and fuel filter.  Have your battery, alternator, and fuel pump checked as well.

Your worst case scenario is that your transmission really is on its last leg; which would require a rebuild or replacement.  But it's best to have a transmission shop inspect it for you to pinpoint the cause.
Good luck!