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I want to hook up ESP8266, which has a 3.3v logic level to my bare-bones Arduino (basically a minimal interface for the ATmega382P IC).

I can power my circuit at 3.3 V without a 5 V regulator so will the voltage of the logic level also be 3.3 V?

I don't think there is a tiny boost converter in the IC... but I'm uncertain.

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The logic level is the same as the voltage you supply the chip.

You can think of the IO pins as tiny switches that either connect the output pin to the supply voltage or to ground (when in output mode) or compare the incoming voltage to an input pin to a percentage of the supply voltage (typically <0.3×Vcc for low and >0.6Vcc for high)

So yes, if you run the chip at 3.3V the logic level will be 3.3V logic (or more specifically < 1.1v for low and > 2.2v for high).

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