A few things and about temps with this storm
1) An occluding low is becoming vertically stacked, so you need to worry less about the surface low having a good track, but getting skunked by an 850mb low 150 miles west of you flooding the region with warm air
2) The precipitation will be very, very heavy so it will naturally cool the column
3) The deeper the low, the more the pressure gradient force overwhelms the coriolis force resulting in a more direct high->Low wind direction. In other words, winds will be more northerly than one would expect from a low in that position
4) The low eventually will lose northward momentum and pinwheel eastward, so whatever push of warm air there may be (which there wont really) will be gone
The big thing I'd be worried about if this thing keeps coming north is a big-ol wedge of dry air just being hurled northward into somewhere over eastern LI/southern New England