Tossing a new idea into the mix - - - InfraRed Thermal Sensor. I'd imagine it would have a very fast sensing rate. Have that compared to a previous temperature lagging by 2 or 3 seconds - that might be faster than anything I've read so far. Perhaps more accurate. But then again, pointing it at a cold wall then at a warmer wall - you'd get an alarm if the warm wall (or cold wall) were more than the threshold you set by programming.

bot IR sensors and programming are things well beyond my skill level, so I might be completely wrong. But I'll let others consider the IR sensor thing.

 

Here's my humble offering :-



Just twiddle the pot until the voltmeter reads about half the supply voltage. A 1°C temp change then results in about 10% change in the meter reading.

 

Could always use a thermistor in a ac coupled circuit to provide a reference signal to a comparitor. This would block DC but allow through low AC (changing) frequencies to provide a reference to a comparitor circuit. This is basically a electronic differentiator so faster the rate of change the more volts would pass through. https://www.britannica.com/technology/differentiator#ref91686

 

Here is a variation of what I had in mind.

The temperature sensor consists of a resistance bridge R1-R4. R2 and R4 are identical thermistors. I suggest using 10kΩ @ 25°C but almost any value can be used. R5 variable resistor is to balance/offset the bridge so that there is a small voltage difference between the two arms of the bridge. This is going to determine the temperature threshold.

While R2 and R4 are both thermistors, one thermistor (R2) is subjected to moving air while the other (R4) is shielded from draft.
When R2 experiences a sudden temperature drop, the resistance of R2 will rise and the corresponding voltage into R6 will also rise.

R7 is the reference voltage with a slower time constant. You need to adjust R5 so that the voltage at R6 is just below the voltage at R7.

The LED D1 will flash ON or OFF depending on the polarity of IC1 comparator inputs. Interchange the inputs if required. Feed the output of the comparator into a flip-flop for manual resetting, or into a monostable for automatic resetting.

 

Your mention of Paranormal got me to thinking and reading a little. While I have no desire to hunt ghost I have watched enough TV programs based on the subject and have to admit some of the tools they use are pretty interesting. Interesting enough I tried a Google of "Ghost Hunting Tools" and saw some pretty cool stuff. All of this got me to thinking about something you mentioned, the cost of some of these gadgets. With that in mind I am staying with my initial suggestion of using a micro-controller. There are dozens of them out there and literally thousands of working code samples and tutorials making it easy to learn. Here is a simple example of what I am getting at.

This board is an Arduino Uno available globally at a reasonable cost.


Many members here also have used the Chinese knock off versions with the same results as the actual genuine board I linked to. A nice feature here is the main chip is an Atmega 328P and as you can see is a DIP package. You can buy just the chips and sockets with boot loader installed for a few bucks. Program the chips as pictured above then place them in your projects. My thinking here is many of the Ghost Hunter tools I viewed can be assembled using micro-controller chips. Here is an example of a temperature monitor I put together.



The little blue device is my temperature sensor, there are dozens to choose from but the pictured one is a DHT11 temperature / humidity sensor which uses only 3 wires and cost about $2.00 USD.

Finally a display and liquid crystal displays are relatively inexpensive. Here is an example.


The pictured display is a SunStar 2004A model which is overkill but I had one so used it. 20 character wide and 4 rows and only a 4 wire interface to an Arduino or similar uC. The entire affair is modular so it is like putting blocks together with a few wires. Both the sensor and display are 5 volt powered off the Arduino board. The Arduino board i9s easily powered using a 12 volt battery (7 ~ 12 Volts). Anyway, it's something to consider if you want to ever expand your ghost hunting tool kit.

Ron