I agree that
暑くてお酒を飲みたい sounds a bit unnatural, but the following is fairly usual:
- It was hot and I wanted to drink alcohol, but there was nothing when I checked the fridge.
Some examples with ...て...たい without being followed by additional phrases:
- 暑すぎて裸になりたい It is too hot and I want to go totally naked.
- 恥ずかしくて穴があったら入りたい I'm so ashamed, and want to hide in a pit if there is any.
- 失恋して死にたい I got my heart broken and want to die.
After thinking and a bit googling about ...て...たい, it is true that such sentences tend to become unnatural, but it can be ok especially when the intended meaning is it is too ... that I want to ....