I have two identical ceramic coffee cups, but when I put them into the microwave (oven) with the same amount of water, for the same amount of time, the handle of one cup is discerningly hotter than the other. Why is this? I speculate that it has something to do with density because when I tapped each handle with a spoon the tones were very different, but again that is total speculation.
Ceramic objects are porous, and always have unglazed areas to allow internal gases to escape during firing. Look at the bottom of your cups; their bottom surfaces are almost certainly raw ceramic.
But, just as gases can escape through these areas, liquids can be absorbed into them. Run your cups through a dishwasher, and they may start to accumulate water inside the ceramic's pores. And bingo: water absorbs microwaves and heats up.
My guess is that the cup that heats up has absorbed more water, perhaps by cooling down in a saucer of water (sucking in water), or being washed bottom-up in a dishwasher more often. Although I've never tried it, putting the cups in a warm oven for a while might drive out the absorbed water, reducing the unwanted heating.