Was the temperature exposure within design specs?
How hot did it get?
We don't really know for sure what temperature the unit was at. Objects can absorb sunlight and get hotter than the surrounding air, so it could have gotten hotter than the 89F air temperature.
It's hard to judge temperature from touch because metal objects conduct heat, and potentially a lot of it, efficiently to your hands while insulating materials don't, so metal objects feel much hotter.
However, one potential indicator of its temperature would have been its effect on your hands. Animal tissue starts to cook at about 115-120F. That "threshold" temperature for injury is reflected in the safety guideline for setting water heaters. Above 120F, you can get second and third degree burns (although at 120F it would take a number of minutes). Below 120F, you can still get first degree burns (source)
So it suggests that the unit was likely under 120F if you were able to handle it, and didn't receive any form of skin injury (no more than transient effects).
This is far from definitive, but it may give you a way to judge ballpark temperature relative to 120F (unless you have calloused hands). In this case 120F is a fortuitous number because it also happens to relate to the unit's specs.
There are a number of temperature-related specs. There is a temperature range in which it's designed to operate, and another (typically wider range), in which it can be stored in a powered-off state. These ranges are usually published and readily available, even included in the specifications section of the user manual. That wasn't the case for this model (only the recommended operating temperature is listed).
I contacted ASUS tech support. Their recommended range is 0~35C ambient temperature both for operation and storage, with an upper limit of 50C (122F).
For perspective, that doesn't mean that the unit is guaranteed to self-destruct the moment it hits 123F. It's the limit that's guaranteed to be safe (probably with some margin). ASUS just doesn't make any promises above that temperature. The farther you get above 122F and the longer it remains there, the more risk there is of potential damage.
Risks from exposure
So if the unit didn't exceed 122F, you have absolutely nothing to worry about. If it exceeded that, but not by much, you probably still have nothing to worry about. If it exceeded it by a lot there's a possibility there could have been some damage.
Of course the likelihood of that is much higher if you're located in an environment like @user.dz describes. And if it reached temperatures well above 122F, you would probably have had a hard time handling it and not getting burned.
So worst case, suppose it did get exposed to damaging temperatures. What could have been affected?
- Not the kinds of things you expressed concern about in the question. The electrical connections are exposed to far higher temperatures (molten solder), and greater temperature fluctuations during manufacturing.
- An internal battery might be the item most sensitive to heat; it could shorten its service life.
Other parts that could fail would be anybody's guess. There's nothing you can do about components that have a shortened service life except deal with it when the part fails. But you can put the unit through its paces for hours, or even a day, to guard against infant mortality (detect it not prevent it).
If it doesn't fail quickly out of the box, there's not much useful you can do to predict failure or worry about it (other than normal precautions you would take anyway, such as making backups).
There is absolutely no reason to discard the unit out of concern that it could damage connected equipment. It's possible with any piece of equipment for a defect to damage connected equipment, but there's no reason to expect that this exposure to heat would create such a problem.
The unit cannot create surges. So a surge protector would be irrelevant in terms of protecting other equipment from this unit. However, it would be safe practice to plug all of the equipment into a surge protector to protect everything from external power line surges.
Similarly, there is no reason to expect that the heat exposure would create a condition where the unit could affect the wall outlet power. Any defect that did affect the power, wouldn't damage other equipment, so you wouldn't buy a UPS for that purpose. But again, using a UPS for all of the equipment would protect everything from external brownouts or power loss (or surges) on the power line.