Would ice/heat therapy help relieve a strained sternum?

Try. I do not know how severe is the lesion in your sternum. Assuming is not serious...In general ice or heat (topical) works as antiinflammatory. Inmediately to injuries we prefer cold so if there is any bleeding will stop. After few hours heat or warmth is the most common anti inflammatory but some people prefer cold. Make sure there is nothing else like rib fractures or any other pathology. Part 2.
Maybe. There's no harm in trying. I generally find ice to be more effective if an acute injury. Apply for 20 minutes 3-5 times/day in the first week. Be careful applying directly to the skin, as frostbite may occur.

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Will ice / heat therapy help a strained sternum?

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