Electronic – How to extend the output (high) time of the circuit (retriggerable)

I need help with the design of a timer delay circuit for the output of a sensor circuit which can keep the output HIGH for an adjustable time range (about 1 to 10 min), after the digital output of the sensor circuit goes LOW.
Also, the timer should be restarted automatically if the output of the sensor circuit goes HIGH again in the middle of the timer operation.

I saw many different power off delay timer circuits which used the 555 IC, for example, this circuit, but I can't find a resettable timer circuit.

More details: in my case the sensor circuit is a temperature circuit with a LM35 sensor and after it triggered on adjusted temperature, the output went HIGH (12V) and if the temperature suddenly drops below the trigger point, the output will go LOW as well(it contains hysteresis). I need a time delay after the output of the temperature circuit in order to keep the output HIGH for the adjusted time range, and, if the output of the sensor circuit goes HIGH again, the timer interval's must be restarted and it must wait until the signal goes LOW again(like in the motion sensors's delay circuit which id active while it's sensing motion)

-I know it is easy to do it with a microcontroller but I still need to learn more programming .
-It's not possible for me to learn programming at the moment ,so maybe a retriggerable monostable is what I want ?

Below is diagram of the temp. sensor:

^{simulate this circuit – Schematic created using CircuitLab}

schematic according to RoyC answer:

^{simulate this circuit}