Seasons without an axial tilt?

Let's assume we have an otherwise Earth-like planet orbiting a star just like our own. Our planet has an axial tilt of 0 degrees, meaning its axis is perpendicular to its orbital plane.

Could this planet have seasons based solely on where it is in its orbit? My thought was to increase the eccentricity of the orbit, so that at aphelion it's significantly further away from its sun than at perihelion. But the question becomes how much eccentricity do we need to get seasonal variations similar to what we're used to on Earth? And is there even time for the planet to cool enough on its way to aphelion and winter?

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Seasons without an axial tilt?

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