I am not sure that the time of year makes a lot of difference as far as heat is concerned as it is so near the Equator.
As far as rainfall is concernd, I went in May and had no rain at all.
I stayed on Sentosa Island at the Shangri-La Rasa Sentosa and the view was fantastic, looking out over the Western anchorage. You will probably need to be on floor 5 or above to be above the trees.
However it is NOT CHEAP
Be sure to take the ferry to Kusu Island from Marina South but do not miss the last boat back at 16:00 Mon-Fri, 16:30 on Sat & 18:15 on Sundays and holidays. There are few facilities on the island so you may want to take food and water with you.
Have a great time