What header size for a 36" wide window?
it depends on a lot of things:

1)  dead load above
2)  live load (do you get lots of snow, rain, etc.)
3)  wall finish (for practical reasons you may have difficulty changing the header on a stucco wall, which is what it looks like from the cement stains on the interior of the sheathing boards)
4)  material.  steel is much stronger than wood.  spruce is stronger than pine.

in a 2 x 4 wall, you can do a double header construction with a 5/8" ply liner between them as a spacer.  given this, the fact that you are increasing the span from 20" to 36", then the span will be almost twice what was there before, but its still only 36".  generally, you need a 2x6 double header minimum for just about any scenario, so if you are worried about it, go to a double 2x8.  here in ontario, lintels under 2x8 are not permitted (table a-12), but your span is so small it doesn't even fit the minimum requirements.  just use a doubled 2x8.  its overkill, but thats the best way to build anything.