OK, if I have read your post correctly, you have a 2ft cold water you want to convert to tropicals?
I would do a thorough substrate vacuum (just to clean it up as goldfish are messy) then add the heater. No need for a complete water change. When I set up my African tank I cycled it using goldfish then threw them out in the pond and added the heater to the tank. Once it was up to temperature the Africans went in.
Leave the algae for the BN. If it doesn't like your particular algae, you will have to clean it off but, if you're lucky, the BN will do it for you.