First of all, as a speaker of American English, I would rarely say
I'm feeling hot/warm/cold.
This present progressive use of to feel is used for other things, such as
I'm feeling sick
At any rate, I could say
I'm hot/warm/cold.
if I wanted to report on my personal status.
But in many situations I would report on the temperature of my environment when I feel hot/warm/cold. Thus
It's hot/warm/cold/chilly (in/out here).
(Could you fix it so that I'm not hot/warm/cold/chilly?)
So, yes you can say both It's hot or It's warm. And you can say this to either report a fact
It's hot. It's 40°.
It's warm. It's 30°.
or to indicate that you feel hot or warm. But feeling is subjective, and what is hot to one person may be warm to someone else.
Note I can remark on other facets of my environment, such as
It's humid/drafty in here.
but I couldn't say
*I'm humid/drafty
I think we are missing the point some what, and the Professor, as expected, is correct.
It is a 4 point scale
Hot... warm... cool... cold
However when cooling or warming we can only say (use) 3 points on the scale.
Cooling mode.... Hot ... cool... cold
Heating mode....Cold ...warm... Hot
Because we cannot say
1) we are warming whilst cooling something even though warm is cool relative to hot
2) we are cooling whilst heating something even though cool is warm relative to cold
This is completely illogical, and as an engineer I have know about it for years.
Note It is important to remember that this is only the case for a transient temperature (whilst raising or lowering the temperature) Static temperatures can use any of the 4 points on the scale. However, the Professor does note this distinction.
Regarding what a native speaker would use is a bit more complicated.
Heating a room (not Hotting) using the boiler or furnace for example
or
Cooling a room using the air con.
warm the oven before use .... raise the oven temperature to crisp the chicken skin........ Let the pastry cool in the fridge for half an hour...... Chill the wine before serving.
All the above words and many more are in everyday use to indicating a change in temperature.
Best Answer
It is always acceptable to use "spicy".It is most common to use "spicy" or "hot". I agree that "hot" can be confused with temperature so my go to word is "spicy".
Sometimes foods will be labeled "hot and spicy", common in descriptions of food in restaurants.
"Chili" is not only used to describe peppers but also used as common stew. In America I usually only see it occasionally on salsa labels.
"Pungent" refers to a sharp smell or taste but it's usually only used with regards to smell.
"Piquant" is more formal and something that could be found in a food critic's vocabulary.