[amanbhu]

If in the thermometric titration between NaOH and HCl , the temperature of HCl added is always same as the temperature of the mixture , how will the temperature of mixture change? differential or constant rate of change?

[Borek]

Try to calculate temperature change dT for dV titrant added using simple heat balance. I guess it should be obvious if the difference is linear or not.

At least that would be my line of attack.

[amanbhu]

which equation is to be used for heat balance?

[Borek]

Heat lost = heat gained.

This is one of the very basic things done in the general chemistry class (or in physics class, where it is taught depends on where you live). Have you ever solved problems like "what is the final temperature of the mixture if 5 g of ice at -10 °C is put into 20 mL o water at 25 °C"? You need exactly the same approach here.