Differing battery temperatures, rather simply a warm/hot connection indicates that the batteries have different electrical properties such as different actual or nominal capacities, or different internal losses.
The warmer one might be better or worse than the others, but at any event if the difference in temperature is significant, then I predict a short life for some or all of the batteries.
If one battery is newer, then it will probably have slightly lower internal losses, and therefore require fewer AH to charge it. Since the batteries are in series, they all receive the same charging AH. This results in the newer battery being overcharged and becoming warmer.
Alternatively, an older battery may have reduced capacity and therefore be overcharged before newer batteries in the same series string are fully charged.
It is a false economy to replace only failed batteries in a series string.
All should be replaced together for best results, and care should be taken that all batteries are of the same brand, manufacture date, and initial state of charge.
In case of a fleet of similar golf carts, then old batteries from different vehicles might be combined as one battery string, but old and new batteries should never be mixed in the same series string.
