Jupiter provides a distance variance between the Earth and the Sun of 1%. How does this affect the temperature on earth, in a cycle of about 10-11 years?

Answer

If the mutual position of Sun-Earth-Jupiter would have an effect on the climate on earth, then this should not happen every 12 years, but every 399 days, so every 13 months and a few days, because that is the period between more or less equal positions in terms of Sun-Earth-Jupiter. For example, the earth passes between the sun and Jupiter every 399 days (it is said that Jupiter is in opposition). So, if the mutual orientation of Sun-Jupiter-Earth were to have any effect, it would have to be with that period.

But I don’t think that effect is there :

It is not that Jupiter provides a distance variation. The Earth’s orbit is not a circle around the sun, but an ellipse, hence the small variation during the year. Jupiter has nothing to do with that.
The gravitational force that Jupiter exerts on the earth is 25,000 times smaller than that of the sun. So also the influence on the orbit of the earth. The effect of Jupiter on the “coldness” of our winters is therefore nil. Because you know, the Earth is closest to the sun on January 4, and furthest on July 3. So in the winter, when it’s cold with us, we stand by the sun! This is of course because the seasons have a completely different cause, namely the tilt of the earth’s axis opposite the vertical direction around the orbital plane. This tilt is 23°. In summer the Earth bends its northern hemisphere towards the sun, in winter the earth bends its northern hemisphere 23° away from the sun. That difference of 46° (maximum) causes the seasons, and that effect is much stronger than that small variation in distance from earth to sun. You understand, since Jupiter’s effect on Earth’s orbit is another 25,000 times smaller, Jupiter has no effect whatsoever on the “depth” of winter.