The "broken green paste" you removed was conductive paste, and must be replaced if you are to avoid damaging the CPU.
As for what is happening at the moment, your CPU us overheating, dropping to a slower clock rate to avoid burning out, and then going back to speed as it cools. Though this may protect it in the short run, cycling the temperature like that will damage it in the long run. Buy some paste, and fix the problem properly.
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