This sounds like the transmission fluid is overheating because the cooler is not managing to cool it down sufficiently.
First, drain and flush the radiator. Whilst the cooling system is drained, change the water pump (it is probably very old and no longer efficient). (If you are changing the water pump, it is a good idea to change the camshaft drive belt unless it is quite new - if you change the belt, fit a new tensioner as well).
Refill the cooling system, adding the correct fresh anti-freeze, and bleed the system properly. Now see if the transmission has improved. If not, check the level of fluid, and smell it to see whether it is burnt. If it does seem burnt, drain it and refill with the correct fluid (Esso/Mobil LT71141) - nothing else!!! See
here.