It all depends on species…
Shrimp tolerate a wide variety of temperatures but temperature tolerances vary between species. Most will tolerate normal tropical aquarium temperatures, but some require higher temperatures and others are quite happy at temperatures lower than most tropical fish will stand.
Because shrimp keeping is a young part of the aquarium hobby, estimates of what temperatures a specific species like vary between sources. For example, the Amano shrimp is a common, well known shrimp in the hobby. Planet Inverts gives a temperature range for this species of 68-82F, while shrimpfanatics gives a range of 10-28C (50-82F) and most books on the aquarium hobby have no detailed information on aquarium shrimp at all! It is also noticeable that different captive-bred color varieties of the same species are sometimes given as having different temperature ranges. This is possible if the color varieties came from different areas or were kept under different captive conditions for long periods of time, but it is not very likely. It makes me suspicious of the information’s accuracy.
What can one do in such a situation? Pick what seems the most likely estimate for the shrimp you wish to keep. This is usually the parts of the range that overlap between sources. In the case of the Amano shrimp, that would be 68-82F. Watch your shrimp. Are they dying? Are they eating enthusiastically? Are they breeding? Adjust temperatures until your shrimp show the full range of healthy behaviors. Once you have this information, put your results up on the net and let other people know. In an area of the hobby this new, we all have the ability to add to what is known.
For those of you trying to pick a shrimp species, here are temperature ranges for shrimp with non-standard temperature tolerances. All information here is from Planet Inverts.
Aquarium shrimp that tolerate cool water (minimum less than 70F):
Amano Shrimp Caridina multidentata 68-82F
Bee Shrimp Caridina cantonensis “Bee” 64-78F
Caridina cantonensis “blue tiger” 69-81F
Caridina cantonensis “crystal red” 64-78F
Dark Green Shrimp Caridina sp. “Dark Green” 68-82F
Glass/Grass Shrimp Palaemonetes paludosus 64-85F
Golden Bee Shrimp Caridina cantonensis “Golden Bee” 64-78F
Neocaridina heteropoda 64-82F
Orange Bee Shrimp Caridina cantonensis “Orange Bee” 69-81F
Red Cherry Shrimp Neocaridina heteropoda “red” 64-82F
Red Tiger Shrimp Caridina cantonensis “Red Tiger” 59-81F
Snowball Shrimp Neocaridina cf. Zhanjiajiensis var. “white” 69-82F
Tiger Shrimp Caridina cantonensis 59-81F
Caridina cantonensis “white bee” 64-78F
Shrimp that require high temperatures (minimum 75F and up)
Brown Camo Shrimp Caridina sp. “Brown Camo” 78-85F
Cardinal Shrimp Caridina sp. “Cardinal” 78-85F
Harlequin Shrimp Caridina cf. spongicola “Harlequin” 78-85F
Orange Delight Shrimp Caridina sp. “Orange delight” 78-85F
Red Goldflake Shrimp Caridina sp. “Goldflake” 78-85F
Sulawesi Shrimp Sp. name not given, new intro. 80-82F