AMD states that the operating temperature range for the Athlon TBird is 0 - 90 degrees Celsius.
Of course, the higher the chip speed the hotter it will run. My 900 TBird runs at 32 degrees idle, about 42 degrees under normal use (Word, AOL, VB, VC++), and tops out at 50 degrees after 3 hours of full load (games). If I remove the covers, the temperature will drop by about 4 degrees. I am using an AVC model 112600 HSF (AMD approved).
Your temp of 56 degrees seems high for the clock speed. Is this at idle, or heavy load? Do you have enough ventilation in your case? You should have a front intake fan, the output fan from the power supply, and a second case output fan in the vicinity of the processor. The major heat generators are the processor, the motherboard voltage regulators (usually near the CPU), and the video card. All this hot air will pool around the processor. You cannot cool the processor with hot air!
Your temperature of 56 degrees is not dangerous, but is what you would expect of a 1.1Ghz machine. You can do better.