There is absolutely no reason you can't do what you are trying to do with an LM35DZ instead of a thermistor; the problem is not with your choice of sensor, the problem is with the circuit...
At first glance at least, it seems odd to me that you would be using an NPN transistor but having it sourcing current to the load... and having the feedback be the base voltage of the transistor, rather than (for example) from a current sensing resistor... a BJT is essentially a current-controlled device, so driving it with a gate voltage proportional to temperature is not a great way to control output current... Granted, once you get the amplifier polarity right it will at least be relatively proportional, though not linearly... It seems to me this current control circuit is not going to be very consistent, since it's effectively open-loop with respect to the current going to the load... And if you need a particular operating current, it'll require tweaking the pots just right, and probably drift with time, temperature, phase of the moon, etc...