Does the sun have cycles causing temperature changes on Earth? Can the Sun go through seasons or cycles to cause a temperature change? 

Could the Sun have to go through any kind of thermal cycle to change the climate on Earth and by how much?
The Sun's magnetic field is way too weak to have any measurable effect on the Earth's orbit. The sunspot cycle does produce a small but detectable signature in the global average temperature (about $0.2\sideset{^{\circ}}{}{\mathrm{C}}$). Over a billion-year timescale the Sun is getting hotter as helium builds up in its core.