Using a 10K ohm thermistor as a 5K
Typically I want the real R=28k (3 degree celsius) to be read by the micro controller as 24k (6 degree celsius)

This part is pretty easy. The resistance of two resistors in parallel is as follows:

RPARALLEL = 1 / (1 / R1 + 1 / R2)

So you want to solve this:

24k = 1 / (1/28k + 1/R)
24000 * (1/28000 + 1/R) = 1
0.8571 + 24000/R = 1
1 - 0.8571 = 24000/R
R = 24000 / (1 - 0.8571)
R = 168 k

But 168 k is not a standard value so you might have to use 169 k.
28 k in parallel with 169 k is 24.02 k. So the error is much smaller than the &quot;slop&quot; in the resistor values. Should be fine.
Note: this will make the controller think that the temperature is 6 C when the real temperature is 3 C, but it will also cause temperature errors all across the temperature range. It is up to you to make sure this does not create a problem. I don't know how the system works or what the temperature information is used for. So don't blame me if something goes wrong. ;-)