Which is the densest gas known?
Perfluorobutane is inert and has almost twice the density of sulfur hexafluoride. It is non-toxic enough that it is used in fire extinguishers and injected as a contrast agent for ultrasound. Boiling point: $-1.7\ \mathrm{^\circ C}$.

Perfluoropentane is similar and rarer but somewhat higher density $(\sim13\ \mathrm{kg/m^3})$ in proportion to its higher molecular mass. Its boiling point is $28\ \mathrm{^\circ C}$ (uncomfortably warm, but your thermostat can go that high). This is the densest gas that strictly meets all the criteria in the OP.

If we relax the criteria a bit:

Perfluorohexane is just over the boiling point limit at $56\ \mathrm{^\circ C}$, but it has a molar mass of $338\ \mathrm{g/mol}$ which makes it slightly denser in gas form than tungsten hexafluoride ($\ce{WF6}$).  It's also inert and non-toxic, unlike $\ce{WF6}$.

The ultimate gas density would be uranium hexachloride using depleted uranium and $\ce{Cl-37}$, with a molar mass of $460\ \mathrm{g/mol}$, which makes it over 50 % denser in gas form than tungsten hexafluoride, and 3 times denser than sulfur hexafluoride, but it has a boiling point of $75\ \mathrm{^\circ C}$, decomposes on contact with air, is toxic and slightly radioactive.