Causes of global warming

A typical answer would look like this:

"...the Sun's output changes so slowly and solar variability is so slight (less than 0.00425% of the total energy per year on time scales of days), that continuous monitoring by state-of-the-art instrumentation is necessary to detect changes with climate significance. Scientists theorize that as much as 25% of the 20th century anticipated global warming of the Earth may be due to changes in the Sun's energy output. Systematic changes in irradiance as little as 0.25% per century can cause the complete range of climate variations that have occurred in the past, ranging from ice ages to global tropical conditions. For example, scientists believe the "Little Ice Age" that occurred in Europe in the late 17th century could have been related to the minimum in sunspot activity (and a correlated minimum in total solar irradiance) that occurred during the same period."
NASA Cosmicopia citing ACRIMSAT website (2000)​

Note that this is not due to "heat increases as its fuel is consumed" - the output of the Sun varies anyway.

Have you seen:
https://xkcd.com/1732/