Boiled shrimp hardly fall in the live shrimp category. It's a good idea to check the temperature regularly, and to drop a piece of ice into the shrimp tank. You don't want frozen shrimp either. Some anglers purchase a small, insulated ice bucket or shrimp carrier, and place the smaller container inside a larger, ice chest, packing as much ice as possible around it. Shrimp will keep for a day or two with this method.
Some fishermen carry shrimp in live bait buckets, the same type as used for fresh water fishing.
If the bucket is the typical, double style, it's no problem to change the water supply and thus the oxygen. However, with a single bucket, water changing is a little more difficult. These pellets generate oxygen when placed in the water of a bait bucket, and help keep the shrimp alive. However, it's still advisable to change the water regularly, particularly to keep it from getting too hot. Dumping a large number of shrimp into a small container guarantees a high mortality rate.