That may help some, but the majority of the magic will happen in your filter. So, you have a couple of options.
1. Get some filter media from an established filter, and put it in the filter you have on your tank. This will really speed things up for you.
2. You will be doing a lot of
water changes.
You said earlier water parameters were good. Do you have a
test kit? To test water parameters?
Ammonia,
nitrites and
nitrates?
Also, take a look at this. It explains everything you need to know about the nitrogen cycle:
Nitrogen Cycle
You have a great start by upgrading him to a larger, heated and filtered tank. Just need to get you the rest of the way there!