A heat sensor that powers an LED with no controller
Assumptions:


The question is really about accepting input from a temperature sensor, and indicating it via an LED's intensity, without using a microcontroller. 
The temperature sensor shown is merely indicative, any temperature sensor that can be used for this kind of implementation would do.




The temperature sensor linked in the question has an I2C digital interface. I2C requires some form of processor or microcontroller at the receiving end, to query the device, retrieve data (the temperature in this case) and process it.

Instead of such a digital temperature sensor, an analog sensor would allow an implementation such as described, i.e. lighting an LED based on temperature, without using any microcontroller. 

For example, the Analog Devices TMP37, 20 mV / oC output.

This output voltage can be amplified using a DC coupled up-amp, then used to drive another op-amp as a current driver, such that the current at the output will vary by the sensed temperature. If the temperature sensing range is wide enough, the voltage amplification can be dispensed with, and a single op-amp as a voltage controlled current source can be built, using the temperature sensor's output as the control signal.

LEDs are current-driven devices rather than voltage driven (as long as their required forward voltage is met), in other words the intensity of light output varies non-linearly with the current through it. Hence, this arrangement would vary the intensity according to temperature.

Some careful tuning of the amplification stages will be required, to achieve the right intensity gradient against the desired temperature range, but that is not too complex.

Such a circuit can be easily built on a breadboard.