Touching Fire is not Being Burned
No, no, and yes, respectively. For the pain, obviously, your flesh is not being seared or punctured - you'd feel a liquid, more or less viscous than water, maybe it has little bubbles or something. Your body has to actually be harmed before you 'touch' pain. Note that the sensation of touch is not the same as actually touching the object or liquid - it wouldn't deform around an invisible hand or anything. Traps or spells or creatures that detect even the faintest touches wouldn't detect anything, as they aren't actually being touched.
Heat and cold - you would be able to feel that the object is cold or warm, you would not personally feel cold or warm on your flesh. I.e. your hand wouldn't burn or feel burnt from touching a furnace, but you would feel the heat of the furnace, as that is 'touch' based.
To expand on this, by my understanding of specii, pain is a haptic sensation from the destruction of flesh, which to my knowledge of specii and how it was viewed at the time, is still correct. You got the pain sensation from being burned, not from feeling something burning hot. If you divorce the 'feeling hot' from the 'destruction of flesh', you don't get the pain, just the intense heat. Notably the sensation of intense heat would make you feel pain by our modern understanding of neuroscience, but, Ars Magica.
The description for the DnD 3.5e psionic power Touchsight would be a useful guide for the sort of information you might receive. No colour, no nature of items automatically - you'd have to get the shapes and work it out from there what was going on. I'd include a Per check to make sense of what you're receiving, get useful information, just as from your normal senses. But perhaps with a higher threshold if you don't keep this sense active much.
Also, a blind mage who uses a Sun duration InIm spell to do this would be a cool character to play.