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We present a model for cosmological inflation which has a natural "turn on'' and a natural "turn off'' mechanism. In our model inflation is driven by the Hawking-like radiation that occurs in Friedmann-Robertson-Walker (FRW) space-time. This Hawking-like radiation results in an effective negative pressure "fluid'' which leads to a rapid period of expansion in the very early Universe. As the Universe expands the FRW Hawking temperature decreases and the inflationary expansion turns off and makes a natural transition to the power-law expansion of a radiation dominated universe. The turn on mechanism is more speculative, but is based on the common hypothesis that in a quantum theory of gravity at very high temperatures/high densities Hawking radiation will stop. Applying this speculation to the very early Universe implies that the Hawking-like radiation of the FRW space-time will be turned off and therefore the inflation driven by this radiation will turn off.