blossom drop in pepper plants can be caused by several things...i'm fighting it right now on some of my peppers too, but i think for different reasons than you.... i believe that it is getting too cold at night; 45 is a damn low temp. for peppers, they tend to like it warm...this is from University of Illonios extension...
Hot PeppersCayenne, large thick (70 days to harvest)
Cayenne, long, slim (73 days)
Jalapeno (70 days)
Red Chili (84 days)
When to Plant
Peppers are best started from seeds indoors in late winter and then transplanted into the garden after the soil and air have warmed in the spring.
The plants cannot tolerate frost and do not grow well in cold, wet soil. When night temperatures are below 50° to 55°F, the plants grow slowly, the leaves may turn yellow and the flowers drop off. Raised beds, black plastic mulch and floating row covers may be used to advantage with peppers to warm and drain the soil and enhance the microenvironment of the young pepper plants in spring, when cool weather may persist.