How does the precession of the Earth's apses affect climate?
During the 20th century, the global mean temperature in January was 12°C while it was 15.8°C in July. This is a bit paradoxical as insolation is currently about 7% higher during January than it is in July. So why is July warmer than January?

The solution to this apparent paradox and the answer your question (how does apsidal precession alone affect the climate) are one and the same: The uneven distribution of land and water between the northern and southern hemispheres. The northern hemisphere has about twice as much land as does the southern hemisphere. Continental climates exhibit much more seasonal variability than do maritime climates.

That worldwide insolation is greatest in January and least in July is a bit irrelevant. What is more relevant is the length of the seasons in the northern hemisphere. Right now, summer is longer than is winter in the northern hemisphere because perihelion is in early January. This situation will be reversed in ten thousand years when perihelion and northern hemisphere summer solstice coincide. Looking at precession only, glaciation is much more likely during periods where northern hemisphere summers are short and winters are long.