Learn English – “Drop” vs Drop off”

Tom is the best expert ...

Assertion of a fact. Where there are agreed criteria then there's no need to hedge an statement.

Djokavic is the current number one male tennis player in the world

When criteria are less certain, or we ourselves are not sure of our facts, or we wish to be modest by appearing to be uncertain of our facts we may use I think

I think Djokavic is the best male tennis played of all time

I think that the population of the UK is 50 million (actually 65 million)

This formulation implies that we are open to correction and discussion

Adding would softens this further, emphasises that we are uncertain

I would think that the population of the UK is greater than 50 million

The I would have thought formulation is normally used in a context where some information has recently been given. Depending upon the context it may imply that we are actually contradicting the information, or that we are expressing surprised acceptance.

I think Tendulakar is the best batsman of all time

I would have thought Bradman had a better record

that was disagreeing, suggesting that by some criteria Bradman is better

The current UK population is 65 million

Oh, I would have thought it was only 50 million

but now I've changed my opinion (this implied but not said)

that was agreeing, I thought it was 50 million, but I accept your statement of 60 million is correct. We could just say

Oh, I thought it was only 50 million

With pretty much the same meaning, the slight difference being that the second case implies it was actively in my mind, whereas the would form could imply that I hadn't really formed a solid opinion until now, but I would probably have guessed 50 million.

As your comment indicates we are indeed into shades of meaning and idioms. In these cases the tone of voice will often differentiate the meaning.

I would have thought Bradman had a better record

Would probably said with a questioning or challenging tone and raised eyebrow.

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