I've never encountered one quite so stuck, but it's too late to be hammering bits of metal, so I'd give both the cups a good squirt of penetrating oil (or WD40 if that's all you've got) and come back to them in the morning.
Heating/cooling isn't likely to do very much since the frame and the cup will be expanding/contracting at the same rate. Only works if you can heat/cool one and not the other, and since they are mechanically connected this is difficult - you'd have to change temperature of one component really quickly before the other 'catches up'.
I've never encountered one quite so stuck, but it's too late to be hammering bits of metal, so I'd give both the cups a good squirt of penetrating oil (or WD40 if that's all you've got) and come back to them in the morning.
Heating/cooling isn't likely to do very much since the frame and the cup will be expanding/contracting at the same rate. Only works if you can heat/cool one and not the other, and since they are mechanically connected this is difficult - you'd have to change temperature of one component really quickly before the other 'catches up'.