Does anyone have a Schiit Yggy DAC?

It has enough room around it. The room is kept about 74 degrees.  The dac runs hot, not warm.

Since 'warm' / 'hot' are relative and we may have different sensitivities, can you take a temperature reading at the 'hottest' (to your touch) surfaces? 

In my experience the Yggy runs warm (I left it on continuously) but not hot. I would have been able to keep my fingers on it for a long time.

What kind of thermometer would get an accurate temp?

The Yggy is spec’d as consuming 35 watts (although a rear panel marking that can be seen in a photo at their website says 45 watts), and measuring 16" x 12" x 3.875" and weighing 25 pounds. 35 (or even 45) watts dissipated in a component of that size and weight should not result in the component getting anywhere close to being as hot as you describe. And the presence of numerous ventilation holes in the Yggy’s top panel further reinforces that conclusion.

Either the power consumption spec is drastically wrong or the unit is defective and what Schiit told you is wrong. Consistent with some of the previous responses I’m inclined to believe the latter.

Regards,
-- Al

Getting anyone at that company to speak with their customers is
not an easy task. They should have explained the product is a dual
purpose machine. Coffee warmer and sometimes DAC. 
I do credit them for truth in advertising.