Would it be possible, within say three to four centuries, to breed
these elephants into more obedient creatures?
Yes but choose females for the actual work. When ready to mate, males are too driven by their hormones to be trusted. They should be kept for breeding only. Possibly castrated males would be usable and in general, castration causes some level of gigantism. This would present an even more fearsome aspect to the enemy. You would castrate bulls that showed evidence of dominance at a young age. Castration would both calm them down and simultaneously remove them from the breeding pool.
Why do castrated animals grow much larger? https://www.quora.com/Why-do-castrated-animals-grow-much-larger
By selective breeding you can achieve tameness of a fairly vicious predator in less than 50 years. It doesn't take centuries for a relatively fast breeder.
In the 1950s a Soviet geneticist began an experiment in guided evolution. He wanted to show how domestication works
As pointed out by AlexP, Elephants don't breed so quickly but the OP specifies that we have centuries to work with. It's practicable to make substantial progress in that time.
However you may not need to with elephants. They have a gentle compliant nature apart from males when in must. This can be seen when baby elephants are rescued after their mother or herd have been driven off or killed (often by poachers).
These young elephants easily form a bond with humans and other animals
Orphaned Baby Elephant Forges Unlikely Friendship That Will Melt Your Heart http://www.directexpose.com/orphaned-baby-elephant-bond/
WARNING - If you google "training young elephants" then you will discover that this is done regularly and may involve unpleasant methods including separating the calf from its mother and worse.
acquire tolerance of lower temperatures, comparable to European
This would take longer. However elephants do have body hair and breeding for this to be longer could conceivably be done in centuries. In any case elephants are hardy creatures. Hannibal took them over the Alps.
Breeding would happen by selecting for baby elephants that kept their hair for longer into adulthood.