well, Delta T doesn't need to be in Kelvin, either way 25*C-10*C=15*C and 298K-283K=15K, the change in temperature will remain the same either way, all you've done is waste time by adding 273 onto the temperature which is commenly given in *C
ΔQ has units of joules .The base unit of mass is the kilogram - 1 gram is 10^-3 kg and you need to stick to this.
Units of ΔT would be kelvins obviously.
To get a consistent equation where the units on both sides must match up you would need c to have units of Jkg−1K−1 - you got the units of Q wrong to start off with.
It can be either, the difference is the same regardless of the unit because 1°C = 1K