Contrary to what continuum says (he's usually spot on, though), it's quite normal for a HDMI to VGA adapter to be fairly warm. Ballpark figure for a HDMI to VGA decoder is around 200 mA at 5 volts.

There’s a six-foot HDMI cable included and the audio, USB, and VGA cables are all attached to the converter box. Accepted input resolutions range from 640×480 to 1920×1200 while output ...

Atlona Technologies have announced the HDAiR, a wireless USB to HDMI or VGA adapter which allows cable-free connectivity to a display from up to 30 feet away. Using UWB, up to 720p or 1440 x 1200 ...

The Monitor Adapter could also be used along with new ultra-thin laptops, such as the Lenovo X1 Carbon–which has no HDMI or VGA port–to connect to displays or projectors.

Yeah, this adapter stuff is crazy. $80 if you want to plug in a USB device and be plugged into power at the same time for a $1200 laptop. Meanwhile dropping the thunderbolt standard too.