I don't know if you can sweat methadone out of your system, but if you really want to try, maybe a sweat lodge would be a good start.
For many tribes, the sweat lodge is a purification and renewal ceremony, and many people swear by it. I have found it useful for other purposes, but never thought of using it to try to get drugs out of my system...that's what I get for not asking.
To build a sweat lodge, create a space that will fit at least two people using fallen branches, brush, etc. Put a rug or two on the 'floor'; you might also want cushions. Don't use good ones. Cover the structure with blankets (again' use old ones), and use brick or stone to create a sort of open box.
Build a fire outside of the sweat lodge, and use it to heat a number of stones. Carry these with tongs into the loge and place them in the 'box.' Take in a container of water and a dipper.
Get as comfortable as you can inside. Pour water from the dipper over the hot rocks. I have seen many formulas for how many dippers of water and why; I don't think this matters in the context you are talking about.
DO NOT DO THIS ALONE. There is a possibility that you may become overheated, even to the point of passing out. As long as you are conscious and sweating (THIS IS IMPORTANT! IF YOU STOP SWEATING YOU ARE GOING INTO HEAT STROKE AND THIS CAN KILL YOU!!!), you are probably OK. Be careful, and drink a lot of water before and after.
If you try this and it works, I'd like to know...