A pool blanket is really designed to slow down the evaporation heat loss through the surface of the water. This is the main form of heat loss. This also means it slows down the water loss through evaporation.
If your pool is in direct sunlight, you will benefit from the radiated heat of the sun passing through the blanket and warming the pool. This is especially true in the warmer months of the year.
There are a few issues you need to be aware of with a pool blanket.
If we have some warm sunny days, and you lift the corner of the blanket, you will feel the water is nice and warm. Take a dive into the pool and you will be suddenly shocked at the cold water about 400mm below the surface of the water.
You need a way to try and mix this hot water on the surface with the cold water underneath.
If the weather becomes very hot, the pool water starts to get very hot.
It really is not fun when you come home from work on a stinking hot day and want to cool off in the pool, only to find the pool temperature is at 36 degrees.
You will need to constantly monitor the pool temperature and remove the blanket in hot weather, or replace the blanket when the weather is about to turn cold.
Forgetting to put the pool blanket on the pool before a cold windy night, will seriously shorten your swimming season.
The use of a pool blanket only, is fine, but it does not really extend your swimming season, it just makes the water a bit warmer in the warmer months.
If your pool is shaded in any way, the warming of the water will be very limited.