I'll focus on planetary temperatures here. Be advised that this is a simplified approach; changing one variable often affects others when it comes to climate.
Incident solar radiation (basically, whatever sunlight actually hits the planet) scales relative to the inverse square of the distance: halving the orbital radius will result in four times the radiation. This makes for rather significant differences between aphelion (the farthest point in the orbit from the sun) and perihelion (the closest point). Ideally, actual orbital data would give the most precision, but finding proportions and using Earth as a point of comparison is fine for this purpose.
To test for radiation at aphelion and perihelion, you need the proportions compared to the normal (the average radiation over the course of an orbit, here assumed to be equal to Earth). The relevant ratio is something like (D+f)^2 / (D-f)^2, where e=f/D; D is the semi-major axis of the orbit (the longest axis between opposing points of the ellipse, or simply the radius if it's a circle). Since we're just trying to find the proportions, D can be taken as simply =1, which means f=e, making our lives easier. In your example, you end up with ~1.12/0.88, or ~1.27, or 27% more radiation at perihelion compared to aphelion.
Planetary temperatures scale with ^4 of incoming radiation: there are other factors, like albedo and greenhouse gas effects and so on, but the radiation is the figure we're actually changing, so that's what matters right now. Taking the fourth root sends us back to ~1.06 from that 1.27 figure, but these temperatures are calculated in Kelvin, not Celsius. Apply that increase to Earth, and the average planetary temperature goes from ~288K to ~305K, or 15C to 32C, obviously catastrophic: a small eccentricity change has huge effects. Of course, that's if the lowest point (aphelion) was equal to Earth's average case; picking the right figures in calculation is vital.
If you go back to the perihelion case, 4rt(1.12) nets ~1.03, producing a more reasonable increase to 296K. For aphelion, 4rt(0.88) nets ~0.97, to drop to 279K at the other extreme. Over the course of a year, you're thus dealing with a planetary temperature swing of ~17C, from 6C to 23C, whereas Earth remains with a relatively steady 15C year-round due to its nearly circular orbit. Those are mighty swings; if your planet's year is too long, it can definitely cause big problems, but that might be of great interest for whatever story you're telling. Bear in mind that those are average temperatures over the entire planet, not for any particular region: there's obviously going to be hot spots and ice caps and all the rest.
Impacts: the negligible axial tilt means you won't have true seasons, but the eccentric orbit will effectively produce distinct "hot" and "cold" seasons. As for climate impacts? Expect most of your climates to be temperate or especially continental, since those are the climates that deal with large swings in temperatures. You'll have little to nothing for truly tropical conditions, since the "cold" season is going to plunge almost everywhere below 18C under your present parameters, and snow will show up in rather lower latitudes than we expect on Earth. I predict much larger glacial melts (and freezes) as well, so rivers fed by that are likely going to be fast and powerful flows compared to what we see on Earth. Still, you're within the bounds of habitability in most regions, although deserts in the "hot" season are probably death traps.
A word of caution: in practice, of course, such changes can be somewhat muffled by tweaking other parameters like albedo or atmospheric content, etc., so this result isn't necessarily final. Calculating surface temperature tends to be a messy exercise if you step away from Earth defaults, but it can be done. You can plausibly stipulate that, say, there's a little more (or less) of specific elements in the atmosphere to modify the greenhouse effect as needed without significantly distorting your world as far as anybody can tell.