concerning charecteristics of resistive heater

I am doing a project on TEMPARATURE CONTROL using PID.

I am using a resistive heater and i am giving constant dc supply to the haeter for certain time.

In the design of a PID controller for my project, I need a mathematical relationship between the SUPPLY VOLTAGE to the hater and the OUTPUT TEMPARATURE of the heater. Below are the specifications :

Supply dc voltage to the haeter : V
Resistance of the haeter : R (at room temparature)
Temparature of heater element: To at room temparature
mass of heating element : m
specific heat of haeter : c
time for which voltage supply is given to heater : t seconds

Below is the way i tried to get the equation. Please mail me if my approach is correct or not.

Heat input to the heater in time 't' is, (Qin) = (Supply Power)(time) = [(V*V)/R].t

Heat input to the heater in time 'dt' is (dQin) = [(V*V)/R].dt ---- (1)
Heat absorbed by the heater element = mc(dT) ------ (2)

------(1) = -------(2) + Losses (Neglect the losses)


So, T = [t/mcR](V*V) + To

Please mail me urgently as your advices are valuable in my project

Thanking u,
Ramesh Babu