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Even though a long lens spreads the solar image over a larger area, it is getting much more energy in to the sensor or shutter, and thus a long lens is considered more dangerous. The heat per unit area is related to the f/stop of the lens, but the total heat hitting is related to the image area. That means up to 100's of times more total heat coming in with a long lens than a wide angle. The on axis vs. off axis makes no difference, because the lens is designed to provide sharp images of nearly uniform brightness all the way to the edges of the frame.
There are three things that can and do get burnt, the sensor if in live view or shooting video, the shutter if it is closed like when aiming or viewing through the lens, and the aperture blades that are close to where the total light from the lens concentrates before spreading back out to for an image. The current aperture of the lens matters, but usually it is wide open between shots. How well the lens is in focus makes a big difference, but usually the lens ends up in focus if it was last shot near infinity. The amount of time the energy is focused in one location matters a lot, and the worst case of that is an un attended lens that ends up pointed for a long time with the sun in the frame.
For wide shots, minimize the time that the sun is focused on the sensor or shutter. Minutes are likely fine, but avoid 10's of minutes. For long shots, you should likely only allow brief time with the sun in focus in one location on your sensor or shutter, like seconds. Then, for sure avoid any possibility that you leave a long lens un attended and pointed at the sun. There are specific reports of people seeing little clouds of smoke coming from their camera, which would lead to a really bad day, and an very expensive repair.
If you really need to image the sun with a long lens, go with a true solar filter, that is made for that use, and is also safe if you look through the lens. Your camera will then be perfectly safe, and your eyes will be perfectly safe, and you will still have plenty of light to give reasonably short exposures.
Note that when the sun is very low near the horizon, its light is going through a lot more atmosphere, and thus a lot more UV and IR are absorbed. That makes both eye safety and burnt cameras less likely, but there is no easy way to know ahead of time how much is absorbed. So you might get away with more, but should still just assume the worst, and continue with the same precautions.
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