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No, you need a cooler rated for that TDP or above.
If it was just a temporary measure, he could downclock the cpu till he got a better CPU fan though.? depending on the OP's skills, and it would kind of help if the rest of his chassis was drawing hot air out of the case well.
My answer would be:
It could, barely, and if it was temporary while your sourced a better CPU thermal solution, few days or so to be safe, but depends on your skills, you would down clock, and slightly down volt the CPU to do this., but there you would need skills in Overclocking, as an Overclocker would know how to set that up, even if it goes against every fibre of his enlightened being.
If you know little about computer, then Black_zions answer .. NO.