[10asartin]

No, do not do a complete water change. Yes, hot water would be bad for live plants lol. Also, definitely do not change the filter media as that is where most of the tank's BB lives.

I would just begin by treating conservatively. Decrease your photoperiod to 4hrs/day, continue to do this until the algae is gone or until your plants begin showing some wear from not enough light.
Personally, I only leave the lights on in my planted tanks for 8hrs/day, but once you get the algae under control you can play around with the times and see what works best for you.
If you find that you still have algae issues, a photoperiod that seems to keep algae at bay is to leave the lights on for 4hrs twice per day with a 4 hr break in between.

 

[10asartin]

You can rinse it off in the bucket of dirty tank water next time you do a water change, but do not worry about it too much. You kill the BB, you kill the cycle, and most of the BB is in the filter media. In most cases it is actually perfectly fine to do a large percentage water change on an established tank if necessary because very little BB actually lives in the water column, it is all on the filter, walls, and decorations.

 

[10asartin]

You can purchase Seachem Flourish comprehensive, which will take care of the nutrient side of the problem. CO2 supplementation can be achieved by Seachem Flourish excel, but I have never used it and can't comment much further. However, I wouldn't go out and spend a bunch of money just yet. If you continue to have algae problems then I would consider investing in these things