Locally, the effect can be much greater than 1 degree C though, even without the feedback mechanisms. Precession has much more significant local effects because 3.4% closer at Perihelion means 6.8% more energy, and that's significant, even if it varies, 3.4% above normal peak summer to 3.4% below normal, low winter, but that's enough to cause a significant change. It's thought that precession is behind the Sahara desert cycle between forest and desert every 13,000 years or so. Precession may be (speculation on my part), a factor in ending ice ages as well, but it doesn't seem to be a factor in starting them, as ice ages appear to begin on roughly 100,000 year cycles and before that, 40,000 year cycles. Source. There's not any good evidence that I know of for ice ages operating on 26,000 year cycles.