I have 3 things to say about that: First, the logic is not flawed, in fact it is extremely elementary. But: second, here you are arguing with me about whether the sun is the cause of warming, and I stated earlier here at least 3 times that that isn't what I was saying! Do you have reading comprehension issues? I was talking about someone else's logic, not about what actual causes are. And I repeated it just for your benefit. But apparently it didn't sink into your skull anyway.
But it is flawed logic. Here's one last try: Think of a car on a level surface. It's motion is determined by Newton's Laws, in particular F = ma. If you press on the accelerator, you apply more force (F) and, as a result, the acceleration (a) increases. It must increase (unless there's a change in mass (m)). If you let off on the gas, F decreases. As a consequence, either m or a (or both) must change. If we assume negligible change in m, then a must decrease. It may still be positive, but it must decrease. The same is true (in principle) in thermodynamics. If the output from the sun decreases (as has been measured), then something must change about the earth's climate - if the sun is responsible for the current warming. Either the rate of warming must decrease (possibly stay positive or maybe go negative) or the mass or specific heat must change. But the rate of warming is not decreasing, therefore either the sun is not responsible for the current warming or (for your logic to make sense), the mass of the earth or its specific heat must be dropping. Have you seen any evidence of either of these happening? (Actually, the earth's mass increases, so we know that's not correct.) Your burner analogy doesn't really relate to the sun and climate change.
Thanks for the link to biocab.org. An, umm, interesting site with, umm, fascinating ideas :). Let's look at some of those ideas: biocab's claim is that TSI has actually increased and he does that by plotting the TSI since the early 1600s and generating a linear trend. But is a linear trend correct? Think about what that means for the MWP that occurred 400 to 800 years before biocab's plot. It was much warmer then, but according to biocab's linear analysis, there was less energy coming from the sun. So according to biocab, the sun isn't that important a driver for the climate, which pretty much invalidates his hypothesis. And, of course, this ignores the question of what happens about 2.2 million years earlier when the sun's energy reaches 0. So linear is clearly an incorrect way to think of the changes in the sun. It doesn't accurately reflect how the sun changes. However, what a linear analysis over 400 years is good for is hiding the actual trends in the sun's output. What biocab's plot does show is that over the last 3 solar cycles (actually, you can extend that back to 5 solar cycles), TSI has leveled off and even decreased slightly. The peaks of the TSI curve haven't changed much, but the troughs are clearly dropping. When you do an actual analysis of this data, it shows the TSI dropping slightly. I'm not sure whether biocab is incompetent or purposely deceptive, but one thing he clearly isn't is correct. I'm reminded of Obi Wan Kenobi's line in Star Wars: "Who's the bigger fool? The fool, or the fool that follows him?"
You haven't shown much ability in physics, math, or logic, and you seem somewhat gullible to fall for a pretty lousy analysis.