It generates the same heat as a AMD64 would do in a 4U case or no case at all, its how you remove the heat, thats the issue. I have several 1U servers using all different cases and none of them have ever crashed in the datacenters i run them in. If your server was switching itself off, then i would guess you didnt do enough testing with it before it went it.
Ive used the cheap queenservers and chenbro servers before which can be had for (100-200£ inc powersupply), whilst im agree that there probably not the single best 1U case you can get and are probably the cheapest 1U cases your going to get, then several that i have are all excellent value for money and ive never had a problem with them.
In the end it should come down to how critical the server is to you, and you should probably pay appropriately for it.