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More info needed. Does all the water need to evaporate, or just the original stuff?
You could add extremely hot steam and get a universal yes, but the way this is worded makes me think it has to be liquid.
All of it.
I never thought about steam. I guess the amount of pressure needed to persuade steam to mix with standing water would prevent evaporation.
Let's assume you're in complete control of the surrounding environment, pressure, gas mixture etc, and can change them at will during the experiment.
I mean, if you can create a vacuum, water at any temperature will boil-freeze. And the ice will sublimate afterwards above cryogenic temperatures, but I'm not sure how fast.
Even if you don't mix the steam with the water, heat will seep in through the surface. At thousands of degrees you bet that water is gone fast - explosively - as long it's not super deep. If this is for drying something, you can add a bunch of other hot inert gasses to dilute or push it out after, so when you cool everything back down it doesn't re-condense.
If you have to add liquid water, it might be impossible, although I can't say for sure there isn't some weird non-linear evaporation effect that allows it to technically work on very cold water. Intuitively, you are always adding more additional water than additional heat, but water is crazy and breaks usual rules for matter fairly often. I'll do a bit of digging and edit.
Edit: Research turned up nothing. As far as I can tell, water evaporation is calculated as being a linear rate. Like the light thing someone else posted, that doesn't necessarily mean there isn't a counterexample, just that it hasn't been found and publicised well enough for a quick search around. So yeah, no wetting away a puddle.