Is it possible to affect Earth's orbit so that, say, aphelion happens sooner? As part of its natural cycle, the sun is currently drifting away from the Earth, it's predicted to reach its farthest point by July 4th in 2020, at which point the distance between the Sun and Earth will start to close.

Do humans have enough power to control earth's orbit so that the sun starts its trip back sooner? I just can't wait for the heat to come back.
Humans don't have this capacity.  The Earth has a kinetic energy of about $10^{33}$ joules, relative to the sun.  Even if we put the total energy that humans use per year into the Earth's orbit (about 10^{24} joules) we still only have one-billionth of the kinetic energy of the Earth.  

Moreover, the annual changes in temperature have very little to do with the distance from the sun, they are caused by the tilt of the Earth to the sun. For people in the Northern Hemisphere, the greatest distance to the sun occurs in the middle of summer when the temperature is usually at its hottest.

While we can't change the orbit of the Earth very much, we have been much more successful (!) at changing the composition of the atmosphere. The build-up of CO2 and other greenhouse gasses is warming the Earth significantly, and we can expect significant harmful consequences from this warming. We might like "warmth" but we don't like the rising sea levels, droughts, floods, and other effects of global climate change.