Fin curling is more or less uncurable, but the good thing is that your fish don't care what their fins look like :). You can stop it, however.
I have never hear of it being caused by cold water. As far as I know it is caused by
a) Really Hard Water (the tap water has lots of minerals dissolved in it)
But most often,
b) High ammonia, nitrite, nitrate levels (aka dirty water) .
The Marina tank in your picture is only a few litres, so realistically you would have to change the water 100% every day if you ever want hope of reversing or at least stopping fin curl.