Time period is irrelevant. Watts are a measurement of power "flow."
The power from the sun and internal natural planetary heating has been dumping into our ecosystem for hundreds of millions of years. And yet, here we are at a reasonably comfortable temperature with a nice atmosphere.
And as I carefully pointed out below, just the tiny natural variation of the solar flux over its cycles is over six times larger than the entire heat output of the human race.
If you have a big bucket with a hole in the bottom, and you pour water into it at a gallon per minute for a year, and the bucket doesn't overflow, and in fact stays at pretty much the same level, you can reasonably conclude that the bucket is not going to overflow. Adding an eyedropper full of water each minute is unlikely to change this outcome.