Does my PS3 not enjoy the summer?

Yes, it should be ok to play the PS3 in an environment of around 30C. The temperature testing done over at geek.com indicates that the PS3 should operate just fine in an environment upwards of 38 degrees Celsius for periods of at least 84 hours (which is much longer than your 5 minutes).

The summer heat should not be an issue. I'm guessing that the problems are due to an issue with your PS3, or maybe an issue with the game disc.

Generally speaking, as hardware heats up the device compensates by lower cycle frequency which leads to slowdowns, but I'm not sure if that's true in your case.

First, let's get the autosave issue out of the way since as Ben Brocka said, it was patched.

Now, for the slow loading and crashes, there is a common bug where going back to XMB causes PS3 to restart. Nothing to do with heat.

If you're worried about heat causing issues, I would get a can of air duster to clean out inside, namely the fan assembly. Next, keep the device elevated so proper airflow can occur. Do not block any fan intakes or outlets. If the system shuts down and the power light flash red and beep, then you can confirm that heating is an issue. Otherwise, I don't think it's the main reason for the issues you're experiencing.