How to connect 15kΩ NTC thermistor sensor to thermostat which requires 10kΩ NTC thermistor
If you want to shift resistance of NTC thermistor, you should do it with another NTC thermistor tied to the same object first thermistor measuring temperature of. If it can't be done, then you need to change biasing resistor in the thermistor's voltage divider circuit of your new thermostat. It is not ideal too, because you can't do anything with expected thermistor resistance curve, but your range is limited enough so it shouldn't contribute much to the error.
Example of why it is bad idea to shunt or offset thermistors (any kind) with fixed resistor:
10kΩ B3500 thermistor:
15C - 15029Ω
25C - 10000Ω
35C -  6832Ω

15kΩ B3500 thermistor:
15C - 22543Ω
25C - 15000Ω
35C - 10248Ω

15kΩ B3500 thermistor + 30kΩ shunt:
0C  - 17825Ω: measured as 11 °C
15C - 12871Ω: measured as 20 °C
25C - 10000Ω: measured as 25 °C
35C -  7638Ω: measured as 32 °C
50C -  5033Ω: measured as 44 °C

As you can see, the offset is pretty large, increasing faster with lower temperature. But if you swap biasing resistor in your new thermostat with correct one, overall error should be in range of 0.5-1 °C max. The correct new value of biasing resistor is 1.5x (15k/10k) if it's connected to VCC or 2/3 if it's connected to GND.
It's probably will be tiny SMD (0402) component in a dense environment, SMD rework station and some aluminum tape can be handy.