Hi Steve, no the water valve I have pictured is a new-old-stock (about 35-40 years old) hot/warm valve. A hot/warm valve has two solenoids just like a modern valve, but the timer never energizes both solenoids at the same time. The warm solenoid mixes hot and cold to provide thermostatically controlled 100F degree warm water. This valve was made for washers with only a hot or warm temperature setting.
If you replace the valve in your '55 with a modern water valve it will be a hot/cold valve. So your water temperature will be tap hot if you select "hot" and tap cold if you select "warm". I don't believe thermostatic water valves are available anymore, Maytag might still have some, but I'm not sure. I think Larry at Modern Parts House has some left too, but they are not cheap.
Another thing to remember if you use a modern water valve in any solid basket washer, there will be no water-flow restrictor in the line, so if you don’t add one, the washer will fill way too fast and overflow many extra gallons of water into the outer tub and down the drain before agitation begins. You can easily add a flow restrictor and I will show everyone how as I’m going to that on the WO-65-2 tonight.