Engine braking downhills

Is it bad for the Automatic transmission to use the engine brake for downhills? I sometimes have to do a long distance and I used to put on the 2nd gear and the tachometer goes sometimes to 4 000 rpm. However if it put too much stress on the transmission, I will use less engine brake, next time.

 

I got a scangauge to test exactly this question. I frequently drive over a high mountain pass and I actually found that my transmission got much warmer climbing uphill than it did engine breaking downhill so I wouldn't worry about it.

 

Oh really? Great news so! We can trust the Scangauge?