Anyone know what is the highest temperature water the roots of plants
can take without killing the plant ?

It varies.

What I want to do is recycle wash water right from the machine to the
garden as the machine is pumping the wash water out. I would try
pumping water from the wash if its set on warm/cold but not pumping
onto the garden a hot/cold wash setting.

I'm just wondering if even a warm/cold setting is too warm for roots
to take. Ever try such a thing ??? Advice welcomed. Thank you.

Depends on the plant -- some are more sensitive than others. I'd be more
concerned about what's in the water -- this is from your laundry machine,
correct? Soap detergents are not particularly friendly to most plants.

James