How long has it been sitting at 1.011? I mean, have you taken multiple measurements over a period of days, and seen no change in the specific gravity?
If it's 1.011 but still has live yeast and unfermented sugar, then you absolutely need to stabilize it (by adding sorbate and sulfite) before bottling, or else wait longer. I just asked about bottling a batch of traditional mead at 1.002 on another thread, and I was warned about bottle bombs -- and rightly so, I fear, because mine wasn't really done fermenting yet. If you're truly certain that fermentation has completely stopped, that's fine -- but how sure are you?
I don't think the temperature at bottling time matters -- if it's unsafe to bottle at room temperature, then in my opinion it's just plain unsafe to bottle. The question is, has fermentation really truly stopped?