Possible but very unrealistic
First I have bad news for everyone: the oceans WILL evaporate in not so distant future, pessimistic estimates predict it happening in barely 150 million years (more realistic predict it at around 800 millions- 1 billion years)! Better start gathering the bottled water!
This mass dehydration will occur thanks to increased solar luminosity, which will increase the temperature of the oceans and increased vapor in the air will kick the Venus-like greenhouse effect. To reach that state surface temperature would have to reach about 70 degrees Celsius. So long and thanks for the fish!
Now, could human-made weapons do similar things? Highly unlikely: most post-nuclear scenarios would suggest rather nuclear winter rather than nuclear heatwave, due to increased pollution blocking the sun. Of course, that would also kick off the greenhouse effect in the end, but without increased solar activity I seriously doubt that it could increase temperature to such high levels.
However this National Geographic article suggests that the beginning of runaway greenhouse effect (which is the vaporising of the oceans and water leaving the earth atmosphere) can kick in with as "little" as putting the 10 times the carbon dioxide that you'd get from burning all carbon, gas, and oil.
In my opinion, the Mad Max shows lack of clean water, no water at all.
Sources: When the Earth will lose its oceans