Basically, both guages are fed from completely different places.
It seems unlikely two completely unrelated guages would both start to lie, simultaneously. Thus the sensible answer is they're not lying, and the coolant and oil simply arent reaching operating temperature, thus the guages dont appear to move.
As a result, it points at the thermostat being at fault. Its odd that it would fail quickly, but for instance if your 30mile drive was motorway, where engine load is low, and cooling flow it very high and very cold, it might well show up a faulty thermostat where driving round town would not. Thus it might appear that one day your driving round town and all is fine, and the next day its down at 60c and wont heat up.
Can you tell me, does the coolant guage usually stick at exactly 90c once the cars warmed up, or does it wander around a bit?