Hi @suesa. If I might, I believe you do not do justice to the miracle of PCR and I would like to shed some light on several aspects that deserve a more thorough appreciation.

First you say:

You then heat it (= denaturation), so it splits into two strands.

Denaturation happens as you point out at 94-96°C That is a pretty high temperature that most biological molecules do not survive intact. The fact that single stranded DNA withstands such temperatures are testimony to its amazing stability.

Tiny pieces of single-stranded DNA (= Primers) attach to these longer single strands (= annealing).

The accuracy with which annealing happens I also consider quite amazing. Not something to be taken with a shrug, IMO

Then, an enzyme called polymerase starts synthesizing a new strand of DNA, matching the one that already exists (= elongation). When that is done, you have two double strands instead of the initial one.

This is the most amazing thing of all. Most enzymes from normal organisms are designed to work at temperatures of up to 43 - 45°. Around 65+ most proteins (enzymes are proteins) start becoming denaturated. This is what happens to albumine when you cook an egg for instance.

Yet here you have a DNA polymerase that is happily replicating DNA at ... 72° ! Isn't that amazing ? It would be like if suddenly your "Spiegelei" turned into a live chicken and sprang out of your plate ! What's the secret ?

Well, that isn't just any vanilla-DNA polymerase that you are using there ! That is an enzyme which has been isolated from a species of bacteria adapted to living and multiplying near hot water sources like this one:

Thanks for the memories (my M.Sc in Mol. Biol dates from 1995 ...)