Terra-forming Triton is when changing Triton to make it support life from Earth. However, disadvantages are numerous. Triton is extremely cold. Triton is the coldest place in the solar system. However, Triton also has advantages. Triton has an abundance of a rocky surface, nitrogen ice, methane ice and water ice. Nitrogen is suitable for all life on Earth. Methane a powerful greenhouse gas. Terra-forming Triton may not be as hard. A great heat source is needed. An artificial heating source around Triton will put major changes in the environment. The methane becomes liquid as a new atmosphere is introduced. Then as Triton becomes warmer, the methane oceans boil into the atmosphere trapping more heat from the sun raising temperatures even more. Nitrogen begins melting then eventually boils making the atmosphere nitrogen and methane rich. The water would still be ice. Once the water ice melts, the heating is done. The heat ring would have to keep the temperature stable on Triton. Triton would need a supply of oxygen reducing the methane but keeping the nitrogen.
See also: Triton Simulation