[KeithsTV]

As a very rough guide to temperatures I've found that at 40C(104F) you can keep your hand on the transformer without feeling the need to remove it. At 50C (122F) you can keep it on but will want to remove it after a short time and at 60C (140F) you'll want to remove it fairly quickly. Above that you won't want to touch it and risk burning your hand.

From what you say it sounds as if the transformer is OK.

I have one of those IR thermometers and they will give a good indication of the temperature but you do have to be careful as the cheaper ones are set up for a single value of emissivity, usually equivalent to a dark surface. A shiny surface at the same temperature would give a different temperature reading. More expensive ones, such as the Fluke we had at work, would allow the emissivity value to be changed. But at that price you can't really go wrong.

Keith