Static Verbs

When verbs have a stative sense it usually cannot occur in a continuous tense.
The lists of verbs that have or can have a stative sense are shown below.
1. Mental and emotional states
Believe, doubt, feel (opine), imagine, know, like, love, hate, prefer, realize, remember, see (understand), think (opine), want, wish
2. Senses
Appear, hear, look (seem), see, smell, sound, taste
3. Reactions etc.
(dis)agree, deny, impress, mean, promise, satisfy, surprise
4. Description, possessions, etc.
Be, belong, concern, consist, contain, depend, deserve, fit, include, involve, lack, matter, need, owe, own, possess, weigh (have weight)

The examples below show that the verb like is always stative, but think can be used statively or dynamically.

1. I am liking you (X)
2. I am thinking you are nice (X)
3. I think you are nice
4. I am thinking about it

The sentence “He is being cold” may or may not be acceptable, why?
In this case it’s really the adjective cold that has a stative or dynamic meaning, linked with be.
If it refers to temperature or sensation then the sentence is unacceptable because with that sense be is also stative and may not be used in the continuous aspect.
If cold means unfriendly, in fact showing unfriendliness through some activity, then be is dynamic and is correctly used in the continuous aspect.

References:
A concise grammar for English Language Teachers (ELT G 0055)
Oxford Practice Grammar (ELT G 0035)
English Grammar in Use (ELT G 0052)

Submitted by Ady, ADS6ME 2006