It depends - sorry, you knew that was coming, right?
What it depends on is the actual raw DC you get and the load current. Those are the TO-220 versions, and I believe that the TO-220 has a 1.5A current limit. It also has internal thermal limiting. They look to be 12V/200ma transformers (??) which would indicate a 15-20% "regulation" sag from no load to full load. If you're running them with 100ma on the outputs, they'll sag nearly to the 200ma full-load voltage for some math reasons.
So raw DC is at most ~17.25V, probably a volt of ripple, so call it 16Vdc. If you're taking 9V out, the regulator will be dissipating the load current times the difference in DC voltage across the regulator, or 7V. So for 100ma load, the regulator will make 7V*0.1A = 0.7W.
A TO-220 can get rid of about 2W in free air. So at 0.7W, yeah, they'd just get warm to the touch. Somewhere about 250-300ma, they'd really need a heat sink, or they'd be shutting down from overheat protection at ugly, unfortunate moments.
Notice how sensitive series regulators are to the raw DC voltage feeding them. If this is only a few volts above the output, they can be remarkably efficient (that is, they don't get very hot). At the same load current, a higher input voltage can cook them. In this case, 23-24Vdc into them doubles the power they waste.
In general, if you can put your finger on it and keep it there, it's not under thermal danger - for "average" values of modern electronic parts.
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