I have grown melons in a cold frame for a number of years, but with little success. I gather they dont like it when temperatures fall below 20C, which seems to have been the problem with recent summers in the UK (having temperatures rise above 20C is difficult on many days).
This is not scientific, but I have noticed that when the sun doesnt shine, the newly formed flowers dont open. They last about 3 days in a half opened state and then just drop off.
When the temperatures are low, the plants seem not to produce female flowers - just male ones.
I hand pollinate with a paintbrush, and have had a few successes over the years, when the weather has turned warm and sunny for a few weeks, but never had more than 2 melons (about the size of a large grapefruit) in any one year, although they tasted beautiful.
This year my wife suggested growing them in a growbag on the south facing kitchen window sill (which is quite broad). After recovering from almost fainting with shock, I did so quickly before she changed her mind, and the difference is amazing.
It is only late May and already I have 4 hand pollinated female flowers with small melons now about the size of cherry tomatoes, and more female flowers beginning to form.
I am convinced that the high minimum temperatures inside are giving these improved results, plus the sunshine levels. We had a few days of cloudy weather and the plants almost stopped growing, but by that time the small melons had already formed so it is not such a disaster.
I am looking forward to eating the fruits in maybe 8 weeks time - fingers crossed for no disasters.