Its not the heated environment that's the problem its the humidity inside which causes the condensation on cold equipment. Usually the humidity comes from cooking or boiling water. Depends on your situation.
If you leave your gear in the case it should be fine bringing it in. Only concerns are when the equipment gets down to single digits. In those cases you should use new zip lock bags (bag them outside) and include a desiccant pack in the bag to adsorb any residual moisture in case you got some snow or ice on the equipment prior to bagging.
Extremely cold weather can also cause permanent LCD damage. Often just using the camera can be enough to keep the internal temperature elevated enough to prevent damage but keep that in mind if you are outside for a long period of time. Pay attention to the temperature specifications for your camera and lenses. They all have minimum operation temps. If you have a failure and it was below the operational temp, manufacturers can wiggle out of their warranty.
Regarding your Carbon Fiber tripod... that should be good down to about -4 degrees F (Induro specification). Below that it can become more brittle and easier to damage and likely would not be covered under warranty.
You might consider also getting some lenscoat for your lenses, especially the 70-200. I use them on my large telephotos, not necessarily to hide or mask them but they are sure easier to work with and hold when the weather is cold.
And finally consider that when moving lenses from one temp extreme to the other it will take some time for the optics to become stable after temperature change. A Canon tech advised that it can take about 1 hour to stabilize. I had issue with a 500mm going outside in cold weather and producing soft images. After about 1 hour it cleared up and we attributed it to the lenses changing shape during the cool down period.
Other than that, keep a spare set of batteries inside you coat and don't put your camera under your coat either to warm it up....condensation and fogged optics..