It isn’t always the chest for everyone, but I do know what you’re talking about.
Since we work so much with energy in tarot, I notice these sensations tend to follow certain patterns. The heart chakra activation occurs most when they’re actively missing you, rather than just randomly thinking about you. The warmth spreading is sometimes just casual thoughts or conscious awareness - something has made them think of you.
If they are definitely physical signs… You might want to read this thread, too.
About reaching out during no contact… sometimes the pull to them gets stronger when you resist reaching out in the 3D.