Japan steps up cooling operation. This is from BBC.
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In this context, to work more intensely on cooling operations. The idea is to go "one step higher" on the scale of effort.
Same idea in "to crank up" (intensify).
to step something up means "to increase the amount, speed, or intensity of something."
In the context of the reported sentence, it means they are cooling the reactor more (to increase the amount, or intensity).