at89atbits, this depends on a lot of factors. Firstly, what chip is this? You would need to see what the datasheets says about the maximum power dissipation, thermal resistance, etc., depending on what type of device it is. 10mA is not enough information to determine temperature rise. You would need to also specify the voltage drop that current is passing through to determine the power dissipation and see if it would exceed the limits or cause a high temperature rise.
As HTA mentioned, an input such as a digital or analog input wouldn't normally take 10mA, so if you are putting that much in it may mean you are exceeding the clamping diode voltage, or the pin is driven internally as an output, etc. But I think you might be referring to the power supply input pin. So again I would look at the datasheet to find out.