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I'm planning my upcoming trip to ride real mountains in Spain on my road bike. So far I used Mavic Ksyrium aluminum wheels but mostly on flat areas.

I'm not confident with going downhill on this wheels because when I do downhill my wheels becomes hot from braking. I'm using clincher with tubes inside and standard Shimano brake pads. Should I be worried? Is it safe for inner tube?

I'm asking because I've heard a story about exploding inner tube from heat :(

I was thinking about going tubeless but never tried this on my current set and I don't want to experiment until its needed.

I'd say that it is more about the braking technique you are using and not the wheels themselves when it comes down to overheating. See the following thread where similar topic is discussed:
What is best for your brakes when stopping at the bottom of the hill?

Have a look at this article as well: Braking and blowouts

The author claims that aluminium wheels get heated up quickly but they also quickly cool down provided they keep spinning (airflow). Thus never brake hard to a complete stop, allow your rims to cool down.

I've ridden couple of Eroica events which are known for heavy climbs and long descends and I haven't noticed anyone suffering from overheat tire blowout (punctures on a rough terrain is a completely different story altogether).

To answer your question - master the braking technique I mentioned and enjoy your trip to Spain!

When people talk about blowouts from braking heat, they're usually referring to latex tubes being used with rim-brake carbon clincher wheels. This combination can indeed lead to blowouts on long, fast descents if you aren't careful. I used to run latex tubes with my carbon race wheels, but after having two tube blowouts, I switched back to traditional butyl tubes and never had the issue again. If you're concerned about heat, just ensure that you're using butyl tubes, not latex.

There really is nothing to worry about. Ksyriums have been popular OEM equipment and mid range upgrades for at least 10 years and 1000's of people are riding them in the mountains every year with no issues.

Personally, I have been riding the same set of Ksyrium Elites since 2011 and have ridden the Alps, Pyrenees, Dolomites and Corsica on them with no issues.

So far, I've witnessed one blowout with a rim brake in the alps. However, the cause was not heat but that the rim was braked through (i.e. a section of ≈ 120° split off). (Fortunately, nothing bad happened, and that guy was in a group that had a van alongside with them)

Take home message: take care that the rims are still sufficiently thick.

The one descent so far where we've been taking some extra caution was going down from the Vršič pass at 1611 m into the Soča valley at 780 m (≈ 9 % for a bit more than 9 km). The first part can be done at comparably high speed so air resistance helps. But the lower 5 km (ca. 500 m of the elevation loss) have one hairpin bend after the other (IIRC 19 in total). While there's decent asphalt in between, the hairpins tend to be done in cobble stone and may have loose sand on top. In other words, forget about using drag to get rid of excess energy. Our bikes were loaded with full camping tour gear (back panniers + low riders in front). On that descent we did stop several times to check temperature (and let the lined up cars and buses pass). While I don't have thermometer readings, we did reach "finger says ouch". We also employed water cooling: wet the rim surface - when you are around, the rim is dry again ;-)

(BTW: I don't recommend Vršič as there was a lot of traffic - everything from bikes over motor bikes, cars to fully-grown motor coaches)

You may be interested in these records of maximum rim temperatures together with whether they did have a blow-out or not.

I'm not at all sure that tubeless tires stand rim temperature any better than the tube variety.