7:44 p.m. on November 9, 2012 (EST)
Islandess,
Over the years, I have tried out and tested a lot of insulated bottles, mugs, and cozies. The vast majority are not worth looking at. Here is a photo of ones I have found to work fairly well:

The one on the left (same one leadbelly shows, I believe) is a Nissan 1 liter. The one in the middle is a Nissan 0.5 liter, and the one on the right is a Primus 1 liter. I have used all 3 in Antarctica and on Denali at temperatures down to -40F/C, as well as in the Sierra, Rockies, NE Whites, and elsewhere.The black and yellow stripe on the 0.5 liter and Primus is electrical tape I used to mark which is my personal bottle and not a group bottle. The 0.5 liter is 14-3/8 oz empty.
The graph below shows a comparison of a bunch of "insulated" containers. In each case, I heated the water to boiling (measured 100C/210-212F), preheated the bottle/mug by pouring the boiling water in, dumping it out, then refilling with boiling water, then put each in a large freezer that stayed between +/-3 or +/-4 deg F, so well below freezing. The constant line at the bottom is the 0°C/32°F, freezing line. The second line from the left (triangles) is a Nalgene 1 liter bottle in an OR Cozy. The two top lines are the two Nissan Thermoses (Thermos company imports them from Japan), with the top one (diamonds) being the 1 liter and second (kind of an asterisk) the 0.5 liter. Note that the cozy cools to 100°F in about 5 hours (still fairly warm to drink), the 0.5 liter Nissan in about 20 hours, and the 1 liter Nissan is still 110°F (hot to the mouth) at 26 hours. Each container remained closed and full except when opening the top to measure the temperature with an electronic thermometer that responds fast. If you are continually opening the container and pouring your drink out, you do lose heat more rapidly, of course. And, if the outside temperature is below the roughly 0°F of the freezer, the liquid's temperature will also drop more rapidly.

I don't have the Primus bottle's curve, but that was what we were using during the 6 days in 2010 that we sat in the tent at Vinson High Camp waiting out the storm. My impression is that it lies slightly below the 0.5 liter Nissan.

As I have gathered the curves, the thing that surprised me was how many of the supposedly great insulated bottles and mugs cooled so rapidly. The one that cooled so rapidly (faster than a Nalgene in a cozy) was a famous brand. Maybe I got a defective one, so I won't name it.
I have checked a number of insulated mugs as well, most of which were given out at conventions with company logos (not the mug manufacturer's logo, so I don't know who really made them). In almost all cases, within a short time ( 5-10 minutes) of filling them with boiling hot tea or cocoa, they were cool enough to drink comfortably, but were cold before I finished the 10 ounces or so of "hot" drink. I do have one inexpensive plastic mug, made by Alladin, that keeps that morning cocoa almost too warm when you are trying to get a rapid start on a 0°F day. I have had it for years, but haven't seen one like it for at least 10 years.