We dissipate heat and entropy to the 2.7 degrees Kelvin cold of deep space. Zero degrees Kelvin is 273.16 below zero centigrade or 459.72 below zero Fahrenheit or absolute zero. 1 degree Kelvin is the same size as 1 degree centigrade. Since the universe is expanding, the cold sink will continue to get colder for ever.
As long as the greenhouse gasses in our atmosphere are kept down, we have no problem dissipating heat. Too much CO2 is bad because it traps heat. You don't have to worry about dissipating heat as long as the amount of CO2 in the atmosphere is right.
All water is radioactive and always has been.
WHERE DID NATURAL BACKGROUND RADIATION COME FROM?
The visible universe [ignoring dark matter and dark energy] started out with only 3 elements: hydrogen, helium and lithium. All other elements were made in stars or by supernova explosions. Our star is a seventh generation star. The previous 6 generations were necessary for the elements heavier than lithium to be built up. Since heavier elements were built by radiation processes, they were very radioactive when first made.
Our planet was made of the debris of a supernova explosion that happened about 5 billion years ago. The Earth has been decreasing in radioactivity ever since. All elements heavier than nickel were necessarily made by accretion of mostly neutrons but sometimes protons onto lighter nuclei. The original nickel was radioactive and decayed to cobalt, then iron. Radioactive decays were necessary to bring these new nuclei into the realm of nuclear stability. That is why all rocks are still radioactive. The supernova made all radioactive elements including plutonium, cesium 137, etcetera.
Radiation also comes from outer space in the form of cosmic rays. Cosmic rays come from supernovas that are very far away. There will always be cosmic rays.
Again: 4 Billion years ago, the Earth was a lot more radioactive than it is today. There is no place in or on Earth or in space where there is no radiation. There never was.
= new reply since forum marked as read