The amount of radiation that the paper receives is not the same in both cases.
Take your piece of paper and stand it up vertically. It receives a bunch of radiation from your source. Now, keeping the bottom edge of the paper exactly where it is, tilt the paper back 45 degrees. Because you tilted it, the radiation that would have hit exactly half way up the paper now hits the top of the paper (since it is tilted back, from the point of view of the radiation source it’s now half as high). All of that radiation that would have hit the top half of the paper now goes over the top of it and misses the paper entirely. So overall the paper only receives half of the radiation that it would have received, and doesn’t get as hot.
The radiation from the source is the same. The cross-sectional area of that radiation that hits the paper has been reduced by half. But it’s hitting a total area that is the same (the paper hasn’t changed size).
Tilt the paper back 90 degrees so it is flat on its back and all of the radiation that would have hit the face now passes completely over it. The paper receives zero radiation (except that the paper actually has some thickness, and the edge will receive some).
ETA: Somehow I missed AndrewL’s post which said essentially the same thing. Sorry for repeating.
