Cadmium Yellow Medium usually is a warm yellow, indeed perfect for what you want to achieve. But cadmium yellows can tend to the cooler, greener side of yellow (this was also a problem for the person posing this similar question). Like any colour, this can vary between manufacturers and lines of paints.
What kind of white did you use? If it's titanium white, a fairly stable and neutral, slightly warm white, it's the cadmium that gives the green hue. If not, it could be that your white is too cool.
Adding a little red to your cadmium yellow, and warming it up that way, should usually work, so I'm wondering why exactly it wasn't when you tried it with your first red.
If you don't mind buying more paint, you could also try the tip mentioned here: mix cadmium yellow light and cadmium yellow deep and you have a wonderfully warm yellow. Or buy the most yellow orange you can find in the store.
Below you can see what Golden Artist Acrylics Cadmium Yellow Medium—"a bright clean color with good opacity"—looks like mixed with white, and what Cadmium Yellow Dark—"filling in the deepest, more orange end of GOLDEN's Cadmium Yellow family"—looks like (the two lowest colour bands in the images). You can see a clear difference in temperature:
[ |
 |