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I think temperature is usually expressed in Kelvin as most of the conversions and constants are also expressed in Kelvin, so it makes it easier for calculations and as for Joules versus Kilojoules, q is usually found using heat capacity which is expressed in Joules.
Usually, the units for entropy are J/K. However, it shouldn't really matter. One thing to be mindful of, though, is keeping your units consistent throughout your calculations. Let's say you are adding up different values for entropies. You want to make sure you are adding entropies that all have units of J/K (or kJ/K, should you decide to calculate using those units).
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