"... ive been told the smaller laptop sizes will not run the programs properly because it will start generating to much heat"
What you've been told sounds to me like the proverbial load of codswollop... Sounds like an attempt to excuse poor cooling design. :-(
For info, our 4-year-old Toshiba Satellite laptop has always been used for considerable video editing, without the slightest problems. Originally that was under Windows XP and with 'only' 500MB RAM.
We recently upgraded it to Vista. No significant difference; possibly a tad slower but hardly noticeable.
We then put a second 500MB RAM card in, making - er - 1GB in all. This significantly improved performance specifically for video editing by about 30% (noticeably less disc thrashing and use of virtual memory) but made negligible difference to other activities such as DTP.
In all cases, that's using Windows Movie Maker and, latterly, Ulead's VideoStudio (v9 or later).
Contrary to what some people say, graphics card performance has *no* significant bearing on video editing performance. Performance for video editing depends primarily on the processor power (VideoStudio supports dual-core processors; few other video edit progs do as yet), secondly RAM.
So in general, any modern laptop with reasonably powerful processor and graphics card (nothing fancy required) should do the job. Recommend 1GB RAM, specifically for video editing. Assuming Vista, I recommend a Home Premium machine which will most likely come with 1GB RAM anyway and also supports 'Media Centre' applications. It may even come with Ulead's VideoStudio bundled (our last Media Centre purchase did), plus something like Nero for disc-burning.
Make sure it has a Firewire socket for connecting a digital camcorder. HTH.