Here's how Eugenie keeps her toddler busy and cool at the same time:
I'm always desperate for things to keep my very active 20-month-old boy busy in the kitchen while I'm cooking dinner. I recently pulled out our old-timey, crank-style ice crusher, and voilá! He and I carefully fill the top with ice cubes, we turn the crank together (it's much too hard a job for tiny hands alone), and I remove and place the top in a safe place. He loves the ice chips that fill the bottom half, and enjoys eating what he's "made". We repeat as necessary, until I'm finished cooking or he's ready to move on. The best part? It's just water, so if it gets everywhere, it's not a problem. You can find old crank-style ice crushers at yard sales, or on eBay for as low as $10.
Or, if you have an ice crusher built in to your fridge, you could just fill a bowl with crushed ice and let your kid have at it. Not quite as fun as the crank, but would do in a pinch.