This a joke, or are you impersonating an alligator?

No, an AND gate is still not the way to drive a relay.

Or, why not test. Buy a standard 74HCxx or 40xx or whatever and connect to your relay. Apply square wave of suitable frequency to the two inputs and check what happens.

Since you don't seem to read the posts here, I think you will be surprised when your chip dies from the release of the induction energy in the relay coil.

Have you figured out what relay to use yet? You really have to. You really, really have to. A relay is not similar to a standard low-energy LED. It is not a 0V or 5V device intended to be controlled by a logic gate.

The conditions in the source code may be trivial, but it doesn't matter how trivial unless the hardware is known. And the hardware can not be known since you refuse to specify the electrical requirements of the inputs and outputs.

Would you tell someone to buy fuel for your car without telling them if it needs gasoline, diesel, alcohol or something else?

The microcontroller may be very cheap. But you may have to add hundreds of dollars of electronics for adapting the inputs and outputs, depending on what sensors or relays you are going to use.

If you expect someone to do this for free, then that person deserves to get valid specifications. If you expect to hire some consultant, then that consultant needs a specification so that you can both agree when the delivery fulfills the requirements for payment.

With your current specifications, you will most probably not receive a working unit (yes, it will be working, but not wark for you) since you seem to ignore so many issues.

Either specify a sensor and say: I will use this sensor, or tell what temperature range, precision and need of calibration you have and let people come with suggestions. But don't ignore this problem and just assume that 0 to 5V will solve any problems. I have access to a lot of hardware capable of reading 0 to 5V, and I know what problems such an input has when it comes to reading temperatures with a reasonable range and precision.