Blowing air through the openings may have made it worse. Depending on how the heat is dispersed and the kind of dust. I just worked on a laptop that has a vapor phase heat exchanger that is like a miniature car radiator with fine fins. Dust and lint combined to form a matted blob that blocked the air flow. It was in the air chamber under the fan. You need to open the computer, remove the fan and inspect. Clean the fan and passages with a small brush and blow out the rubbish. Carefully inspect the small passages.
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