@Miskelley Nancy It's jvery likely that your temp sensor that has drifted a little. I don't know what type of temp sensor your system uses but my guess is it's using a NTC-10K thermistor as the sensor. A thermistor is just a resistor whose electrical resistance varies with temperature at a known rate. They provide more electrical resistance at cooler temperatures and less at higher temperatures. They're pretty accurate and work very well and are inexpensive but they can go out of spec and cause your system to read high or low. Here's a temperature vs resistance curve for the temperature and high limit sensors my tub uses which I know are standard, off-the-shelf NTC-10K thermistors because I've compared this chart to charts for NTC-10K thermistors and they're the same.
So what your system does - if it uses this type of sensor - is read the resistance through the thermistor and then based on its programming, infer a water temperature according to this chart. So at 90F, your temp sensor is supposed to read about 7.5 K ohms but what would happen if it has drifted a bit with age and now reads something higher than that? It would continue to heat the water until it finally reads 7.5 K ohms but the water would actually be hotter than 90F. How much hotter depends on how far the thermistor has drifted.
Is your system going to know that drift has happened and set an error code? Maybe, but maybe not. Your system will likely use the same sensor for both the temperature sensor and the high limit sensor. The only way it can know if the temp sensor has gone bad is compare it's reading to the high limit sensor's reading. Once the difference between what the two sensors read is high enough, the system will set an error code. In this case, maybe the difference isn't high enough to trip the code. Or maybe the high limit sensor has also drifted in the same direction so it's also reading a bit low like the temp sensor. In that case, there would be no way for your system to know there's a problem with either sensor and no error code would be set. You know it though because you set the system to run at 90F and it's keeping the temperature at 100F but your system
thinks the water is at 90F.
Assuming your temp and high limit sensors are actually based on NTC-10K thermistors, the way to diagnose this problem is easy: Measure the water temperature with a decently accurate floating thermometer, use a multi-meter to read the resistance through the sensors and compare the readings to this chart. If either sensor's resistance reading is off from what this chart says it should be then you can be pretty sure what's causing your problem.
Thinking on a more simplistic, practical level, what else is there in your system that could be causing this problem? Maybe a bad motherboard and/or topside control but always eliminate the simple and most likely things before going to the more complex and less likely things. The logical thing to suspect here is the temp sensor and possibly the high limit sensor too. As I said, most companies use the same sensor for both things and if they're both about the same age, they should be both be replaced at the same time because if one is bad, the other is probably bad, or will go bad soon.
My advice is to replace both sensors and that should probably take care of the problem. I'd be darned surprised if it doesn't.