The key to cold weather crops is to not let the roots freeze at the point where the leaves form. The plastic cups I used at night I also kept on during the days to create a heated micro climate. I took them off every third day to let the moisture and humidity out. At night I used a plastic painter's drop cloth to cover everything. I put the drop cloth on around 5 pm. Some day temperatures just broke 40, I kept the drop cloth on there 1 or 2 times for a full day. This created some heat for the bed. It did this on full sun days.
This method saves a few degrees of heat. That is all you need.