What physical property determines how warm it needs to be for ice to change to water

The physical property you're looking for should be the melting point of ice.

Melting point of a substance is a temperature that the substance will change from solid to liquid (melting) , or vice versa (freezing).
Different substances has a different melting point. For example, of ice, the melting point is 0°C, if we keep heating the ice at 0°C, the ice melts and become water.

Make sure don't mix up chemical and physical property, chemical property is the properties that the substance reacts with another substance, such as the property of metals to react with hcl to give out hydrogen gas. while physical properties are the observable properties, and does not gives out new substances such as melting points, boiling points, color, density etc.

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Bc they get tired from playing with other kittens