Depends. Intel made 3 different heatsinks for socket 478. A Prescott 3.0GHz cpu (commonly referred to as 3.0E) originally came with a "X" style heatsink with copper core and aluminum fins quite similar to those used on Intel's LGA 775 Pentium CPUs. The Celeron D for socket 478 came with a heatsink similar to the Prescott P4, but smaller and in a "spiral" pattern mimicking the LGA 775 CPU coolers. The older Williamette Northwoods only came with one style of heatsink, a plain aluminum heatsink with vertical fins. That's probably what your Celeron 1.8 has. A Prescott P4 at 3.0GHz will not like that old style heatsink. You can get by using the older heatsink, but he CPU will be idling higher than if you used the newer Prescott heatsink. A case with good airflow is key.
This information comes from my own observations with a Celeron 2.0 Northwood and a Celeron D 310, and trying both the old and new Intel heatsink designs to see their affect on temperature. The Celeron D's heatsink was superior to the old Intel design, lowering the idle temps of both chips ~4-5 C over the older Intel design.
Celeron D heatsink:
http://www.xbitlabs.com/images/cpu/celeron-d/cooler-1.jpg
http://www.xbitlabs.com/images/cpu/celeron-d/cooler-2.jpg
Prescott P4 heatsink:
http://www.silentpcreview.com/files/images/intel-hsf/intel-hsf1.jpg
http://www.silentpcreview.com/files/images/intel-hsf/intel-hsf4.jpg
Old Williamette and Northwood heatsink:
In case anyone is interested:
the two styles of heatsinks using the LGA 775 Pentiums/Core 2 Duos. The left came from a Pentium 4 EE 3.73 (and is the same what came with my Pentium D 805), the right one came with a Pentium EE 840.
http://www.pcperspective.com/images/reviews/131/heatsinks_top.jpg
http://www.pcperspective.com/images/reviews/131/heatsinks_bottom.jpg
Type of heatsink used on the LGA 775 Celeron Ds, note the aluminum core (which is solid aluminum, not hollow in the center like the copper core in the Pentium 4 LGA 775 heatsink):
http://www.cdrinfo.com/Sections/Articles/Sources/Intel_Celeron_341_346/Images/cooler_base.jpg