Ballpark figure for a HDMI to VGA decoder is around 200 mA at 5 volts. That's a watt. For such a small device, you're going to expect that to make it fairly warm.

An Apple spokesperson told The Verge that Lightning to HDMI and Lightning to VGA cables “will be available in the coming months.” by Sean Hollister Sep 13, 2012, 11:07 PM UTC ...

Adapters are available to connect VGA monitors to laptops that have HDMI or DisplayPort. NPD In-Stat is forecasting shipments of devices with DVI, HDMI and DisplayPort to pass 2 billion by 2015.