I don't recommend the 2CR5 for the RTSIII. Besides the poor response to cold that Walther mentioned, the battery is expensive, can only manage a few rolls, and only allows 3 FPS (not 5) from the motor drive. Use AA cells, with chemistry according to your needs:
Alkaline. Advantages: price, availability, shelf life. Disadvantages: weight, cold weather.
NiMH and NiCD rechargeables. Advantages: price, cold weather. Disadvantages: weight, shelf life, availability.
Lithium non-rechargeable. Advantages: weight, shelf life, cold weather. Disadvantages: price, availability.
I keep stacks of alkaline and lithiums AA cells on hand for all my electronic gear, and only use NiMH for heavy flash events. NiMH/NiCD requires too much fussing and attention for the money saved.