Put Macbook Pro to sleep with HDMI connected to External Monitor? I have conneceted my Macbook Pro (Late 2011) to my recently bought 27'' monitor with an HDMI cable. I have done all the settings so when I close the lid, I can still use my external monitor without any problems.

The issue however is that my Macbook Pro heats a lot when I do that and I also use two devices and therefore have to pay bills for two devices as well. 

Is there any possible way of putting my Macbook Pro into sleep mode so that I can ONLY use my external monitor without my Macbook Pro being 'on' (sleep mode)?

Extra information: 


I use a bluetooth keyboard conneceted with a cable to charge
I use a bluetooth mouse conneceted with a cable to charge 


Both, mouse and keyboard can be used when my Macbook Pro's lid is closed.
Your MacBook Pro can't go to sleep completely as you're using it, however, since you're using it in  "Clamshell mode" (with the lid shut) the internal display will have been powered down (you can tell as the logo on the lid will no longer be lit).

If you want to put the machine to sleep while it's in Clamshell mode, just press Ctrl-Eject on the keyboard you're using and the prompt for putting it to sleep will appear (the specific key sequence is Ctrl-Eject followed by 'S').  You can also put it to sleep via the Apple menu in the top left.