So then what temperature are illusions? Are they just room temperature? If so then if you touch an illusionary person they would feel deathly cold.
Why shouldn't they be room temperatured? If the illusionist is stupid enough to allow a person touch the phantasm it is his problem.
If we are really stretching things we could say the mass of illusion is negligible so that it will heat very fast if anyone touch it, but there is nothing in the spell that says it would start at a different temperature.
Or if you want to get more bizarre, if you put an illsionary rock in hot water, would it heat up?
Why not? I can't see what is bizarre.
Or at what point does contact with a different temperature constitute an 'attack'? If you had enough feels built in for the above rock to survive several attacks, would it heat up?
I don't think heating a object should draw feels unless the heat is large enough to cause a heat critical. Why make things more complicated...if you are using the attack tables then it is an attack.
For physical touch there are special limitations on the illusion that force us to check for breaking feels more often, but heat is something different so I can't see any reason why those special rules would matter.
Or more on the original topic, if you put an ice cube in illusionary tea, would the tea get cold?
Depends on your frame of reference...of course the room tempered tea illusion will be chilled by the ice cube since it take energy to heat the illusion. On the other hand the illusion is fake, so what in the long run is really chilled is the cup holding the illusionary tea, or the table and air around if also the cup is illusionary.
How much heat or cold that the illusion itself can contain depend on the mass of the illusion. It takes more energy to heat or chill a larger object. Since the tea is illusionary and the feels only can sustain very limited weight logic suggest that it's mass is very limited and it will be chilled very quickly.
How fast would the ice cube melt?
Depends on the room temperature, doesn't it? I don't get what the is problem is.
Say it was a blue ice cube, would the tea turn blue by mixing or would you just get a layered effect?
Read the spell description again...you are creating an illusion not real tea. If you want your illusionary tea to make the tea blue then you need an illusion that turns blue at the right time. There is nothing that suggest that your illusionary fluid will interact with the environment.
Just the same as you can make illusionary water that feels wet when you touch it, if you want the fingers to stay wet when they are removed from the water then you need to include that in phantasm you are creating. In many cases you would probably need a separate phantasm for it to work out in case the character moves away from the first phantasm.
To sum up...there is nothing in the illusionist spells that suggest they can produce heat...it is trivial (or require at least very little science knowledge) to tell what happens when the illusion interact with the environment that is at a different temperature if the illusion just adjust to the environment.
The same is very not true if the illusionist can create tempered objects. If the illusionst can will the illusionary water to be hotter than room temperature then he for all purposes has an eternal energy source that will require lots of science knowledge to deduct how it affect the environment. Any heat difference is enough to drive a Carnot heat engine....