Earth would not burn up if it drifted closer to the sun.
The Earth could actually move a lot closer to the sun before total damage took place.
In the summer, the Earth is 94.5 million miles away from the sun.
In the winter, it’s over 3 million miles closer with little to no damage at all.
As a matter of fact, the Earth could be placed in Venus’ orbit, at about 62 million miles from the sun, with surprisingly little damage in the grand scheme of things.
Oh sure, life as we know it would disappear, but the temperature on the Earth’s surface would increase by only about 68°F, not enough to destroy the planet.