and gets my machine too hot.
If WE makes your laptop overheat, your laptop has serious problems.
If I switch to a desktop/tower, what are suggested specs to be able to using the terrain/object editor at a fastish pace?
Any x86 complaint processor with clock speed above 2 GHz. A mid generation P4 will work. All modern I5 and I7 processors will work (obviously) and only some very low clock I3 processors might start to have problems due to the lack of clock speed (remember that WC3 and WE are single threaded so benefit from clock speed and not core number).
On top of that at least 2 GB of RAM is recommended so you can have enough free memory left for file cache use so I/O is less of a concern. All modern computers have at least 4GB so this is not a concern for them.
You need a game speced graphic card for terrain editing. Even a very low one will suffice but it needs to at least have some computational power unlike the purely display driver cards as found in most integrated (except modern AMD) cards or on laptops. Something with only 5-10 gigaflops power may struggle, I would advise at least 100 gigaflops for a reasonable experience as some views can be demanding due to the long draw distance and angel. All modern game cards have >>1 teraflop (1000 gigaflops) in power and will effortlessly run WE and only struggle when you zoom out on a massive map.
I've got an HP desktop with 8 gb RAM, and some token video card. But I need to make a repair to it to get it going again, and I'd really only want it fixed if I knew for sure it would improve speed with the editor by a good margin.
What is the graphic card? If it is anything beyond a graphic adapter it will work perfectly.
WC3 is a very
very very old game. You will probably find Blizzard porting it to Android and Iphone soon.
Frankly with your laptop it sounds like an overheating problem more than a lack of power.
For object editing remember to disable brush list from the menus on the terrain window. The brush list is stupidly slow and will cause some object editor changes (new object, rename object etc) to take 15-60 seconds to make even on the highest end systems. Disabling it will make such changes instant.
For terrain editing you can adjust view distance with middle mouse button. Do this on very large maps to prevent excessive graphic load. WC3 may have stupidly poor and old graphics, but it is also poorly optimized (DX8 tech) and an RTS so not meant to render a 480*480 map from corner to corner.
It is important you turn on vertical synchronization in your graphic card drivers. Otherwise nothing will stop WE rendering 100s of frames per second. Since laptops lack cooling (yes, they are designed to overheat at full load to save cost) this can easily result in the performance problems you are referring to.
Remember that laptops will run in reduced power mode when not plugged in. They can even turn off graphic cards nowdays such as done by the MACBOOK PRO. For optimum performance you really want to be plugged in.