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Just took my 18-200mm VR outside in the garden, and after 10 minutes or so I noticed a big ring of fog developing upon one of the lenses inside. It's not upon the outermost lens but looks to be the second one in, and is like a round halo upon the centre of the glass.

I immediately brought it back inside and removed covers off each end and laid it on the bench fully extended, hoping the condensation will fade away and that hopefully the humidity inside could escape a bit, and now 10 minutes later it's clear again. Was this the right thing to do, and/or is there anything else I should do next time? Is it even a problem, ie. if I'd stayed outside longer would the condensation have cleared once the temperatures of lens vs. outside world equalised?

I've never seen this before on my lenses but am assuming it's from going from inside out into bright sun all at once. Is this normal or does my lens have a problem if there's all that humidity in there? Although I store them within lens bags and then a camera bag I do live in the outback and we use evaporative air conditioning in our homes, plus it's been very wet out here lately.. Should I maybe put it into a box with one of those Hippo tubs that suck moisture out of the air for a few days?

Advice would be appreciated!

What you did sounds OK to me but I'm no expert on this.
What I did want to tell you about is my experience with this lens. This was the 1st lens I got with my camera. I didn't have any others so I wasn't changing it. One day I discovered dust on the sensor. This surprised me as I hadn't had the lens off the camera. When I asked about it I was told that it may have been caused by zooming fast. This lens extends a long way when zoomed causing a lot of air to be sucked into and then pushed out when you zoom in and then out. Dust may have been sucked in and then pushed onto the sensor (or it may have been there all along).
The above is a little off topic, but I hope it explains why this happened along with what you wrote about moving from indoors (air con?) to outdoors.

What you did is fine.
No lens is completely air tight, so over time the air inside the lens will come to the same humidity as the air outside.
If you are in a humid environment, the air inside will be humid. If you then cool the outside of the lens, the humid air will condense on any surface. This is what you saw. It generally goes away once things settles down. Old photography books used to suggest leaving lenses in the taking environment overnight to stop this happening - well it does anyway, but hopefully things have settled down by the time you want to use the lens.

As you live in a normally dry environment, I wouldn't worry about it.If you lived in a normally humid environment, this dampness could lead to mould growing on the lens surfaces over time & I would suggest storing your lens with Silica Gel. The Hippos may well work as well as they are also hygroscopic (suck moisture out of the air) but I have never tried them for this purpose. Unles you live in the tropics though, I wouldn't worry about it.

Yes, I would store it in a sealed container with a Hippo tub or similar to make sure all the moisture has gone. In fact that's not a bad long-term choice if you're generally in a humid environment.

Taking gear that's cold into a warm and humid environment will always risk condensation, and if your lens expands/contracts then you'll bring the humid air into the inside of your lens (which will probably still be colder than the outer lens elements).
The only solution is to let your gear warm up before using it. Generally a closed camera bag will keep the humid air away from it but it will also insulate it, slowing down the warming. To maximise the acclimatisation, put the equipment into a sealed plastic bag (e.g. a ziplock) and get that into the warm environment ASAP.