The reason bait shops use chillers is:
Cold water lowers the metabolism of the baitfish, therefore lowering their need for oxygen, lowering their need for food, lowering the fishes output of waste products. Also cold water holds more dissolved oxygen. All of these factors allow for a higher stocking density of baitfish.
I can't think of a single shiner that needs a chiller to prosper in an aquarium. An unheated tank should be just fine.
Many cyprinids can be difficult to acclimate to an aquarium. Some are very prone to fin and tail rot. Adding a tablespoon of non Iodized salt to the collection bucket, and to the tank that you keep them in can be very helpful in preventing disease.