In my experience the pool warms faster with the cover on. For example, air temp here has been in the 60's and we keep the pool heated to 84 (with the heater). The last couple days the air temp has risen to low 70's and the pool has jumped to 86 during the day with the cover on. In my opinion if the pool water started at 84 it wouldn't rise like that due to 70 degree weather.

My two cents only, your results may vary.