The manager is not doing you any favours, despite what he's telling you. Don't take any crap from him about getting credit, it's not your problem at all. It has a warranty, so you can bung it back as faulty with a receipt at any stage within the 5 years, to get a repair, replacement or refund, of your choice (that's your options over here anyway, the least you're entitled to is a replacement). If the manufacturer doesn't accept returns (which is nonsense, otherwise there wouldn't be a 5 year warranty), it's still your entitlement to get a replacement to a faulty item.
That heat definitely shouldn't affect a PSU, that's only 20°C, which isn't hot at all. Have you probed the motherboard's northbridge and southbridge for temps? I find my northbridge can get very hot during the summer, up in the 60s and 70s, celcius, unless I crank up the fans. Have you checked that all fans are working, including the PSU fan?
Also you should run a memtest, to rule out RAM. You might think it isn't the problem, but our Dell suddenly decided to start randomly locking up until I removed half of its RAM (It came with 256MB, I put in 3GB, exact same specs as the original stuff). It was working fine with the upgraded RAM for about 6 months before the trouble started.
When you say the CPU and GPU temps are fine, how fine is fine after a good Crysis session (I know what you mean about it giving a good workout, it's the best stress test I've found for the whole system
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)? Have you considered you might be putting it under more stress during the day, than during the night?
If it's not the PSU, it could be literally anything. A PC restarting is such a broad problem, you need to narrow it down. The easiest thing to test is the RAM, as you can run memtest and leave it overnight or whatever. After that you need to carefully monitor temperatures while playing Crysis or whatever to get it worked up. Also, make sure that there isn't a BIOS setting that makes the machine reboot or shutdown if the temps get above a certain value. Unlikely, but it could be
Also, no need to be such a dick to those trying to help you. Nowhere does it mention a warranty in your OP.