I have a Fender Super Champ X2, a couple years old (bought it used).
When I first turn it on, it makes a noticeable, but not deal-breaking, swirling/whooshing noise for five or ten minutes until it's "warmed up" and then it's quiet.
Is this something that new tubes will fix? Or is it likely an electronics-related problem?
Five or ten minutes is not tube warmup (which is more like 15sec) but rather the warmup of other circuitry. That may include bad solder joints.
It's often possible to hunt such thermal problems down using a bottle of cold spray (which is specifically used for such diagnosis). Of course, you don't want to reach the hot tubes with that in order not to cause the glass to crack.
Thermal problems are really time-intensive to hunt down. The usual culprit will be a capacitor with instable dielectric.
If your sound disappears in a hard manner, like switched off with a switch, it is more likely a bad solder joint as opposed to a bad capacitor than when it just abates gently.
There is so much broadness to your question. One faulty cable can bring a whole amplifier down, but here are some common factors that you should try out:
Test if there is a faulty tube. You can do this by turning on the amp and set the volume fairly high. Then grab a pencil a lightly tap each tube. If one of the tubes rings or clinks through the speaker then you should look into replacing that tube. Here and here are good visual aids.
Make sure you get tubes replaced by a professional, there are many electrical dangers that can be deadly within amplifiers. Also your amplifier will need to be re-biased and unless your a sound/electrical engineer it's not worth doing it on your own.
Try turning all of the pots on the amp. Sometimes old pots can cause many electrical issues within your amplifier.
Make sure your speaker is getting the recommended power input. Sometimes when people change their speakers they don't check what power rating they best suit and end up having broken amplifiers.
Circuitry issues is a big one. If an amplifier doesn't get covered properly the amplifier ages faster and dust and cobwebs become apart of the circuit.
Overall, it seems to me that you might have an issue with the circuitry that controls the tubes because of the relationship you mentioned between the tube warming time and the swooshing noise. However, I don't think it will be a direct issue with the tubes, rather, an issue with the electrical circuitry because broken tubes tend to create a buzz in the amplifier and other noises.
My suggestion is to take your amplifier into a amplifier tech and get them to run circuitry diagnostics and fix your amp! :)
I have a similar problem with my Super Champ X2. The amp turns on but then will lose output quickly after a few minutes of playing time. Thought it was the tubes but swapping them didn't repair the issue. Took it to a repair tech and he said there are some intermittent solder joints that are being affected by the heat of the power tubes. He got the amp working again but wanted $100 to do the repair. He also said pushing up on the tubes when replacing them can also cause the circuit board to warp causing shorts so be careful when you do swap tubes in this amp. Didn't want to put the $$ into the amp right now (it isn't used very often) and have decided to try using some automotive heat tape (like the kind used to wrap auto exhausts and air intakes) placed above the tubes on the bottom of the amp chassis to see if I can abate the heat from the tubes rising up to affect the circuitry. Worth trying by purchasing a roll of tape from an auto parts store for a few dollars versus an expensive tech repair. Apparently the heat buildup of the power tubes getting into the circuitry is a design flaw with these amps (and probably most tube amps with circuit boards if the heat isn't properly dissipated) and my hope is the tape acts as a heat shield to help stop it from happening.
