I would suggest NOT cooling a monitor unless you believe for some reason your is much hotter than it should be.
If you look at your monitors specs, it will say that the optimum picture is achived after 15-20 minutes. Why you wonder, becuase the monitor has been designed to give the best picture when it is at operating temperature. If you cool it, it will never achieve operating temperaturee, and your picture quality will be reduced.
If you really want to cool it, there is a monitor cooloer our there. It is a small fan that sits on top of the monitor and blows air upwards. As total waste of money IMHO.
my 2 cents.
Moohoo