Try checking what's going on inside the case first - maybe the filter just got clogged or air isn't circulating properly. Sometimes even a thin layer of dust on the cooler seriously affects cooling, and cleaning takes five minutes and helps better than you'd expect. If the case is closed and tight, there might not be enough fresh air intake from outside.
About the temperatures - the previous answer is right that it's within the normal range for this card, but your 87-90 is still higher than the recommended specs. If you want to drop it by a couple degrees without taking it apart, check your driver settings - the cooling profile (Power Limit) might be set too high. You can dial it back a bit and the temperature will drop, though performance will go down just a tiny bit.
If nothing changes after cleaning the case, then yeah, it makes sense to look into replacing the thermal paste, but that's a more involved option. While you're at it, make sure the cooler is pressed firmly against the chip and the fans are actually spinning without any hitches.