Should the transformer be hot when the furnace isnt running? replaced the transformer and it is hot to the touch but not hot enough to burn fingers..
Yes, transformer primaries use electricity (and therefore get warm) even when there is no load on the secondary winding. It's usually just 5-10 watts, and that'll be hot to the touch depending on how much thermal mass it has and airflow around it.
It's normal for the typical cheap 24VAC 40VA transformers used in security systems and security camera get hot enough to discolor their plastic shells, so I'd say it's normal for a similar furnace transformer without a plastic shell will get just as hot even though I've never actually touched or measured mine on my furnace.
I've heard of people using 24VAC switching power supplies instead of 24VAC transformers in their furnaces to save wasted energy. That constant 5-10 watt draw can cost you $5-10 a year in electricity. The down side is that they're more likely to fail vs a transformer, which is not something you usually want to risk on a furnace. Also the power from one is "noisy" and might not play well with a furnace controller that wasn't expecting it.