Speaking for the PW123 and 150 engines.
See a picture of the PW150 air inlet here:
http://www.k-makris.gr/Gallery_2_pics/PW150A_intake.JPG (not embedded due to excessive size). I did not find a similar picture of the 121 or 123 series, but it looks similar enough. There are many vanes, shafts etc. involved that are of course susceptible to icing.
Two methods are used to keep the inlet free of ice: firstly, the intake flange is heated electrically via 115V variable frequency. And secondly, the oil return line from the reduction gear box to the tank is routed through all those vanes to keep them warm. So in order to ensure adequate anti-icing capability, a minimum oil temperature is required.
The requirement of a minimum fuel temperature on the ATR seems a bit odd to me; it must be related to the points of measurement on the engine installation. On the DH8, it is all about the oil temperature.