I've been catching nice fish in the river at the creek mouths where the water has been slightly warmer. How will the cold rain the next few days affect them?  The creek will be fed with cool water now. Will the bass draw back deeper or will the they continue to push after the shad?  Just trying to learn more. 

  Typically they will stick by the bait, whether they drop deeper or not, may be a reaction towards their forage, more than temps.

 I say this as gizzard shad versus threadfin shad are different, and will react different this time of year, When you say "shad" its actually a generic term, so a generic answer is viable.

 This and the fact that you didnt specify what river, your location, largemouth or smallmouth,  etc.  leaves alot to the imagination, and makes it hard for one to answer correctly

Santee river in SC. Chasing largemouth, the river doesn't have a lot of deep holes for them to stay that is not in current of some sorts. It seems they are ready to move into the warmer creeks where the shad are having a fall spawn but haven't really began to move inward yet. Catching better size fish just outside of these great shad spawn locations. 

This time of year I'd still stick around the bait,,... BUT,.. I dont know your area well, so im thinking that,..Maybe, if you post a question in the regional fishing reports threads, someone that fishes your area would have more insight for you. 

 I usually following smelts, herring, and alwives. There are some shad up here, but not enough to be the most prevalent baitfish available.

 

Thanks for your time 

The water clarity and increase in current will likely play a larger role than the temperature change.