Kelly Tan The current high temperatures Even if your sentence were just this, you would need have , but, it's even more than this because you have added something else to it as well by the word plus : Kelly Tan The current high temperatures plus the fact that we've had no rain in recent months have/has contributed This is the combination of a plural noun + a singular noun that will result in plural. Hence, I'd use "have".
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Kelly TanThe current high temperaturesEven if your sentence were just this, you would need have, but, it's even more than this because you have added something else to it as well by the word plus:
Kelly TanThe current high temperatures plus the fact that we've had no rain in recent months have/has contributedT