Hi,
You probably need to rethink that trigger circuit... I think you need to contemplate supply voltages, how battery voltage drops with use, and how inputs work and their voltage level requirements (datasheets are your friend).
Suggestions:
Put a voltage divider on the 9V supply to get the 5V needed for the LM35. Place a 1uF and a 100nF capacitor from V+ (9V) to ground around the voltage divider for a stable supply voltage. If the 9V is a battery that will quickly fall to 7V use an LDO or a TL431 to generate the LM35's 5V supply.
You need a comparator, not an op amp, for the trigger circuit... Anyway, if you have a 741, perhaps you have an LM324 - much nicer to use: +2V to +30V supply and input includes ground. LM35 at 30C is 0.3V - 741 inputs are minimum requirement of 1.5V above lowest supply voltage, the 741 won't 'see' the LM35 input of 0.3V...
You could be 'clever' and use an LM324 with a gain of ~4 and feed that into the 555 reset pin then the alarm is only on over 30C but that would be fussy for you to get right, I think, looking at your circuits.
Other option, easier: get a comparator, or use an op amp whose inputs include ground as a comparator, make the 0.3V reference with another voltage divider and have the comparator set up to go low at >0.3V. Use the comparator output to trigger the 555 with circuit A or circuit BI showed you in a previous post.
If I think of anything better, I will come back.