I have a bread that's laid on the table from yesterday but it's neither cold nor hot, and I want it to become a little bit warm because I like it fresh. What's more fit in this context? Do I want to warm or to heat up or to reheat the bread?
I suppose they are all commonly used and are largely interchangeable in informal settings. You may also want to "toast" the bread which is something quite different than just reheating it.
You enjoy a warm slice of bread.
Let the [frozen] bread come to room temperature, then pop in the oven for 5-10 minutes at 350 degrees for a warm revitalized loaf. - The Best Ways to Store & Reheat Bread: Advice from a Baker.
You reheat it if you had kept it in the freezer. You can heat it up if it was sitting on the table.
Avoid storing bread in the refrigerator, ... When you reheat bread, it actually changes the starch molecules back, but this also means they can go stale more quickly afterward.
If the bread was not in the freezer, "reheat" might not be appropriate. Of course, you could also say "warm up the bread, please". "Reheat" can also work if the bread (that is on the table now) was once heated up before at the time of the first consumption.