Well it all depends on the cause of hearing loss.
If one was born that way then there would be no problems becos the normal ear function usually compensates.
So information is relayed to brain as usual...therefore no real known effect on thought process.
In case of loss of hearing in one ear..one needs to find out the cause..whether it was infective,neuronal or traumatic or part of aging.
Mostly can function normally if the other ear is not as affected ...therefore thought process and actions should not be affected.
But an unproven beneficial side effect of unilateral hearing loss is one can turn a deaf ear to one's wife's nagging!LOL