#1
I know that leaving a guitar right next to a radiator will warp it but I was wondering if where I have it currently will cause any damage to the instrument. The guitar is an epiphone dot studio. the bottom of the guitar is about 40cm away from the radiator. Here's a photo if that helps. http://prntscr.com/dw1g6k (bit of a crap photo i know).

cheers
#3
I wouldn't place any guitar next to a radiator.
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#4
Firstly, is it just balancing on top your desk? Get that lady on a stand or a hard case. And no I would not keep an electric guitar directly by a HVAC unit.

In fact since the guitar is a semi-hollowbody you may want to see about getting a humidifier for you room to keep humidity around 40-60%, which is a factors that applies mostly to acoustics so I am not sure if it applies to hollowbodies, but it would not hurt- especially if your room/the air around your guitar is bone dry.