Hi Soar,
As soon as you move away from the stock cooler you are going to affect the way the motherboard is cooled. If you change to an upright cooler like you or I have done then obviously, air that was being blown downwards from the Stock CPU Cooler is no longer doing so and so you have to improve the airflow over the motherboard by other means to compensate. The most effective way to do this is with a good PC Case with adequate fans to pull cooler air in and then blow warm air out.
There are always doom merchants who want to tell you what can go wrong and whilst their advice is often given with the best of intentions it is only one side of the story. Check through this forum and see how many people actually post here just because they are happy with their builds, not too many.
Leave your shroud in place, I feel pretty confident that it is not going to cause you too many heating problems and, if temperatures do start to rise in the summer months, you could always add a smaller fan to direct air onto the Northbridge and Southbridge chipsets, if needed.
With regard to monitoring temperatures on my system I tend to use CoreTemp and HW Monitor. I also use EasyTune6 and AMD Overdrive for monitoring, but this is usually when I am first putting things together and I use them as indicators so I can see if any of the other monitoring software is showing a major discrepancy.
Through testing I have found CoreTemp and HW Monitor to be the two best programmes to use, at the moment.