Is it worth recapping a 25 year old amp or am I throwing money away?

That hum and thermal dropout you're describing is a classic failure mode for vintage Japanese audio gear. Nine times out of ten, your seller is right that it's just capacitors, but you need to make sure it's not a combination of things. Replacing those electrolitic caps is the standard fix for instability and noise issues like humming, especally if it's old dry components. The fact that one channel fails when hot points toward a failing transistor or possibly a resistor that's overheating and tripping, wich is often exacerbated by the power supply instability caused by aged caps. When you talk to a tech, don't just let them swap the caps and leave. You need them to check the power supply rails, specifically looking at the heatsinks and the voltage regulation circuit. A failing voltage regulator or a leaking resistor in the output stage can mimic capacitor failure and is a bit pricier to fix but makes the entire system more robust. Since it's an old unit, even if the cosmetic condition is perfect, the internal solder joints can be brittle and might need refreshing or a full board re-flow to ensure reliability. Since you're considering a restoration, get a written quote for a capacitor replacement specifically. Then, ask for a second quote that includes a full power supply inspection and testing the output transistors for thermal health. If the tech just says 'rebuild' without specifying what components are failing, you're probably looking at an unnecessary expense. If they diagnose it down to just caps and maybe some peripheral components, you might be in a good spot for bringing it back to life without burning through a huge chunk of cash on a full component swap. Focus on the diagnosis of the specific faults before authorizing any work. If it's just a bad cap, you fix it cheaply. If it's a cracked IC or a degraded transistor, the cost jumps significantly, so getting that scope defined upfront is crucial.

I went through something similar with an old tape deck from my uncle's garage. Had that same low buzzing sound and the repair guy only charged me for a couple hours of labor once he found the bad parts. So from my limited experiance it doesn't have to turn into a huge bill. One thing I noticed after the fix though, the sound seemed warmer to me than before, in a good way. Do these old amps just sound diffrent than new ones once they're working right again?

One thing I'd add from getting a 70s receiver sorted last year is to ask the tech to write down the measurements before and after the work, things like idle current and DC offset, so you have a baseline if anything acts up later. Also tell them up front you want the original parts back in a bag. Mine kept a couple of transistors I wanted to keep for sentimental reasons and it was awkward asking after the fact. Good techs do this anyway, but it sets the expectation that you're paying for a diagnosis, not just a parts swap.

One thing worth doing early is finding a tech who actualy likes old gear, not just any repair bench. I've had amps come back from a general shop where they swapped caps and called it fixed, while the real issue was a dirty protection relay that never got touched. The guy I use now worked at a factory service center back in the day and charges a flat bench fee up front, tells you straight away if it's worth doing. Also, ask them to stick with the same cap values rather than 'upgrading' anything. And expect a wait, mine sat in a queue for three weeks.

I'd push back on the re-flow suggestion in the first reply. Reflowing a whole board 'just because it's old' is how you lift a trace or cook something that was fine. If there's an actual cracked joint, a tech can find it and touch up that one spot. I had a guy talk me into a blanket re-solder job on an old tuner once and it came back with a new problem I hadn't started with. Ask them to prove a bad joint exists before they go waving a iron around the whole thing.

Update: took the guy who suggested finding a tech who actually works on old gear seriously, and it paid off. The shop I found fixed the hum in one visit, something about dried out filter caps. But the channel still drops out once it warms up, so that part isn't sorted yet. The tech mentioned checking solder joints next. Is that ussually a bigger job than it sounds?