Well, it sounds like it will certainly need a current limiting resisitor, preferably close to the ic. From the data sheet:
CAPACITIVE LOADS Like most micropower circuits, the LM35 has a limited ability to drive heavy capacitive loads. The LM35 alone is able to drive 50 pf without special precautions. If heavier loads are anticipated, isolating or decoupling the load with a resistor is easy (see Figure 14 ). Or you can improve the tolerance of capacitance with a series R-C damper from output to ground (see Figure 15 ).
As for sinking the 10mA, it would only ever have to when power is cut to the device. I don't know what happens to the impedance of it's output then. But I doubt that it will take damage. The atmega chip might also drain the capacitor as it has diodes to Vcc on the i/o pins. When the power rails voltage falls because power is cut, the diode will eventually discharge the cap - I guess.