Yes you should always let the cake cool down before removing it from the pan.
If you remove the cake from the pan while it's still hot it could fall apart so allow it time to cool down for at least 30 minutes before attempting to remove the cake from the pan.
Allowing the cake to cool down for 30 minutes will also make the cake ready to put on the icing otherwise the icing will also melt when put on the hot cake.
The cake may also be too hot to touch so allow it to cool down at least 30 minutes before you take the cake out of the pan.
All the bakers that make cakes allow the cakes to cool down before they remove it from the pan because when the cake is hot or warm it can fall apart and crack.