Most cymbidiums can tolerate temperatures as low as 30F. So it might be better if you left the plant outdoors the entire time when the nights are cool, and give it some protection from the sun during the day.
The flower bud cells initiate when the plant is exposed to several weeks of cools nights (40F-55F) and warmer days. They say the key is to have at least a 15F degree difference between the day and night temperatures. A greater difference in temperatures seem to produce better results.
Once the spike does emerge, then it will need to be protected from cold temperatures.
The plant can tolerate temperatures as low as 30F without damage to the leaves. However, the flower buds can be damaged by 35F.
I would not expose my plants to that much cold though, my personal preference would be to keep them above 40F. That is enough to trigger a flowering response, without risking frost damage.
I hope this helps