The only way leaving applications running idle in the background would have any significant effect on anything is if you fill up your RAM completely. In that case, the system will spend a lot of time paging memory out from the disk, which will impact both overall performance (and hence, usable battery life) and temperature--the latter less than the former, but any disk access necessarily causes a decrease in battery life and an increase in temperature. You can generally tell when this is happening because applications you haven't used in a while take a lot longer to become active when you switch to them.
As for how much memory idle applications use, it really depends on the application. Safari or Word can use up a fair amount of RAM when not in use--up to a few hundred megabytes. On a system with only 2GB of RAM, that's a pretty large chunk. Even 4GB may not be enough to handle it, depending on what you're doing. The best way to tell how much memory you're using is to install a memory monitor program like
MenuMeters that lets you continually keep an eye on your RAM usage. If your free RAM ever drops down to below 100MB, it's likely that you're paging. To be sure, you need to check the number of pageouts (you can do this by clicking on the RAM menubar item in MenuMeters). If it's anything but 0, you can be certain that you either need more RAM, or fewer apps running.