This circuit looks like it would do exactly what you want. BUT it may not, as we don't yet know exactly what you want. This shows a 12V fan but 24V would work equally well. This use a relay to turn the fan on and off but you could connect it in the transistor collector if the transistor was suitable. As you have not told us the fan power or current rating we can't be sure about the transistor. That circuit is from here but they stole it from somewhere else to get people to look at heir ads so ignore them.
Here is a direct fan drive circuit that is otherwise similar.
IF you use the 24V for op amp supply and FET you'd need a zener on the FET gate to limit gate drive. A say 12V zener so Vgate - ground ~=12 V would be OK. Change R2 to say 10k. P1, R1, P2 could all be larger with increased voltage. They are non critical as long as you understand how they work and can adjust as required. Circuit and OK writeup here. Note that P2 operation is important. It provides "hysteresis" which controls how much diffetrence there is between fan stop and fan start temperatures.
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CLEVER PROPORTIONAL DRIVE CIRCUIT
But THIS may be what you REALLY want.
You said you wanted to avoid using a PID controller.
You did not say why - and you MAY have meant that you did not want to pay the usual price for one - ie a cheap PIC controller or similar may be OK.
This simple but clever circuit is a P controller :-) (P for Proportional).
You can easily make it a sort-of PI controller
It's clever in several ways - read the referenced text to find out why.
The MOSFET is directly controlled by the NTC thermistor. As the thermistor cools is resistance goes up, the FET gets less drive, the fan slows and the cooling rate slows. Slow the fan too much and the fan can't keep the temperature down, the temperature rises, the thermistor heats, its resistance drops, the MOSFET gets driven harder the fan speeds up the emvironment cools, we are all happy. It will probably "hunt up and down". It will be fun.
The circuit is from here which gives a good writeup. You will probably have to play with R1 - make it a say 10K pot. Put a 12v zener gate to ground on the FET as above or it will die (if using 24V.)
Note that FET will heat when used like this in its linear mode. Max FET power is a bit complex due to non linear motor power_in / voltage / load relationship BUT PFET max is probably about PFAN max when fan is run on supply by itself. eg if this is a 2A 24VDC fan = 2 x 24 = 48 Watt (quite some fan!) then PFET =~~~ 48/4 = 12 Watt. YMMV. Use a heatsink. Take due care. Put FET on heatsink on exhaust side of cooled area if possible. Doesn't hurt your cooling and uses the air flow.
I said you can make it a PI controller of sorts.
Thus: Mount the thermistor on a block of thermally massive material.
To het the thermistor the system has to heat the block.
Once heated it takes a while to cool.
The longer it is at stable temperature the more it settles down.
This may be a strop of aluminum or Al plate or ... .
You can put it in the air flow to change it's cooling "I" value. Or not.
Very rough. more fun. A cap from gate to ground also adds "I" but it needs to be large as the gate resistor is small.
You can make this a "bang bang" controller than switches on an off with the on / off ratio being controlled by thermistor resistance. Then the FET does not get hot and needs no resistance. Usually you'd you end up back with an opamp or comparator but it can be done with just discrete parts. Ask ... .
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One or more of your assumptions is not correct.
You should have \$\theta_{ja} = \theta_{jc} + \theta_{ca}\$, giving \$\theta_{ca}\$ of 30.76 C/W for IC1 and 21.76 C/W for IC2.
With those values, IC1 should have a case temperature of
23 C + (1.2 W) (30.76 C/W) = 59.9 C,
which is pretty close to what you measured; but IC2 should have
23 C + (0.7 W) (38.23 C/W) = 38.23 C,
which is way off the measurement.
A likely cause are if the datasheet's \$\theta_{ja}\$ value makes some assumption about board layout that is not met in your application. If your board doesn't provide sufficient copper area attached to the chip to spread heat away, \$\theta_{ja}\$ will increase substantially. It's also possible that the datasheet value assumes some forced air cooling over the chip.
Best Answer
The temperature control is a well-trodden path. You need to have a sensor of adequate accuracy and a heater of appropriate power level and a temperature controller. I would suggest purchasing a Pt100 sensor (100 ohm platinum RTD), a cartridge heater and a commercial PID temperature controller.
Have a block of aluminum fabricated with cross holes for the sensor and the heater. Bury the sensor inside the block so the tip is many hole diameters in. You could use copper too, but the machinist will be less enthusiastic about the deep holes in copper. The idea is to make the plate thick enough and thermally conductive enough that it is effectively isothermal to the degree that you care.
The heater does not have to be very powerful for this application, maybe 100W.
For the best accuracy you will want to keep air currents off the surface of the plate, so a cover would be a good idea. Insulate the bottom of the plate and use stand-offs so that even if the heater stays on at 100% it cannot cause a fire.
This should cost maybe a few hundred dollars, more or less, depending on quality of control, sensor accuracy etc. and you should be able to hold the temperature steady to within a couple tenths of a Kelvin.