Run MBP with lid off

I have a 13" mid to late 2009 MBP and I broke the screen on it. I replaced the screen but as I was taking the glass panel off, I didn't heat up one corner enough and it cracked, from the top right corner to the bottom left corner D:

I bought a new panel, but it's a cheap/flimsy plastic job, and it's thicker than the original (by about 3 times) so it actually rests on the keyboard when closed, and it's slightly too big so I've had to file it down to fit etc and it's basically in quite a bad state.

So, I removed the lid from the laptop and I've been running it through my TV via HDMI, and I was wondering if there's any adverse effects of this? I know there is no wireless but I can use my phone to connect to my wifi, and the bluetooth was broken when I first removed the glass panel, so that not being available isn't anything new.

I read somewhere that the heat sensor is in the top case, and since it'll be detached it'll run at full fan power when switched on, is this true? And if so, how could this affect my machine?

Thanks

can't you just use it without the glass panel? like the macbook air?

I had the screen replaced on my alloy macbook by the apple store when i broke it (maybe something to consider ;P) but when i got it back and booted up again i noticed my wireless adapter had a little 2 behind it so as my isight and bluetooth connector..
i guess those are the things apple puts in the screen
about the heat sensor, I don't think it will damage your mac, but i would definitely repair it because it is not made to run like this all the time