How old are the batteries, exactly? If they are original to the UPS, they must be at least 3-5 years old, since the 700 model has been discontinued for quite some time. If they're newer, did you replace them with APC batteries? The model & serial number for both the batteries and the UPS would help - there should be a white sticker with barcodes on the UPS (usually on the back) and somewhere on the batteries as well.

Old batteries will experience this issue if left unattended for some time. The unit should have given an alarm about the batteries - either a flashing or solid light on the replace battery indicator on the front display - long before they reached this state. Charging produces heat, but dead batteries don't hold much charge. It becomes a cycle of increasing heat, which causes the gases inside the battery to expand and, eventually, leak out of the battery casing. That's the smell you detected, and that's why the casing is misshapen.

See kbase 564 for the MSDS sheets for APC batteries.

I'm not sure where you're reading or how it relates to APC, but the battery alarms are more related to the capacity and self-test results than temperature. However, the Smart-UPS units do have temperature sensors and alarms associated with exceeded thresholds - assuming you are using the free software or a network card. Are you?

The event is described as "UPS Internal Temperature Threshold Exceeded" and it has a logging, notification, email, command file and shutdown option for this event. It's smart enough to recognize it, but unless you provide a means of notifying someone of the issue, it can't do much.

You haven't mentioned the model & serial numbers of the unit or its batteries. If they are 700va units, they are definitely more than a few years old. If they aren't the original batteries, did you replace them with APC batteries or other brands? It's difficult to tell from the picture you provided since I cannot see the APC logo on the batteries.

It's difficult to offer explanations of what happened with an incomplete version of the story.