no, you can download hard disk sentinel trial to monitor your hard drive temps, be sure they stay below 50 degrees.
Just to add on to this - the optimal operating range is 30-40C. Try to stay within that, it shouldn't be hard with a normal desktop computer. You don't have much to worry about.
No it won't hurt your computer, but I wouldn't recommend leaving it on 24/7 on a daily basis for the sake of the environment.
I think that might be the origin of the "shut down at night" myth. Given how inefficient some older machines were with heat generation, the chance of fire on a cluttered desk and the extra cost of cooling were also likely factors.