Everyone has their own opinion. Here is mine:
1) You do have to worry about heat. The monitor (whatever type you go with) will produce a lot of heat along with the PC (as well as subwoofer if you have one, marquee lights possibly)
2) I do not beleive in removing the motherboard, and PC guts, from the PC cabinet. One reason is that the PC cabinet actually helps keep the PC cooler by creating the contained airflow that the PC cooling fan supplies. Sort of like blowing a fan on you during the summer while you are in an open field and then blowing the same fan on you while you are in a closet - you'll get more of the fan effect in the smaller space.
3) Probably the best thing to do, if your cabinet will be enclosed, is to install 1 or 2 ventillation fans. You can do a search on here and see a bunch of posts on it. Opinions differ here too - some people put in fans that suck the hot air out (fans blowing outside the cab), others put in fans that suck cooler air into the cabinet (fans blowing into the cab). I am partial to sucking the hot air out myself (I figure it helps with dust too, I figure there will be less collected if I am sucking out as opposed to blowing in). Note that some fans are much quieter than others, as well some fans give off a magnetic or electrical type charge (not an expert here), so you may not want the fan too close to anything that will be affected by that.
4) Some people do not enclose the back of the cab, which if you do that then the heat issue isn't that big of a deal.