I've done puddleducks with both my little boys and the pools have always been nice and warm. Littledown do a baby swimming session in the week which is pay as you go - both of mine also loved this.
Individuality swimming do parent and baby classes, their Ferndown pool is nice and warm :)
Most of the public pools locally are quite cold. If you can get into a members club, they’re much better. We are members at The Village and that’s great, we also do lessons with puddleducks at Everlast gym in branksome and that’s lovely and warm.