Translation attempt ; didn't quite understand the writer's コーヒーを一杯飲んだつもりで

Question

私が毎日使っている◯◯線の特急電車に乗るには、五百円の特別料金を払わなければならない。ちょっと高いけれど、蒸し暑くて我慢できない日や残業でとても疲れた日など、「コーヒーを一杯飲んだつもりで」と考えて、つい乗ってしまう。

Here's my attempt at translating it:

In riding the limited Express train that passes through the line I've been using, you need to pay an extra charge of 500 yen. It's a bit expensive but, on days when it's too hot for me or when I'm too tired from overworking, I would just ride it thinking that I had drunk a cup of coffee instead.

What is the correlation of 'drank a cup of coffee' and 'riding the train during hot days or exhaustion from work'? Is it because rather than a regular train, this particular one can help him arrive home faster?

Did the writer imply that riding the train re energizes his body and it's like paying for a coffee? This usage of つもり seemed a bit different than

死んだつもりで、１週間働いている。
あの女の子と友達になったつもりで、一緒に歩いて行った。
歌手のつもりで、大声で歌っていた。

These sound more like "doing ... With the belief of ...."
While the above has a nuance of replacement "doing .... As if you are doing ... Instead"

Answer 1

I think the つもり is like "pretend". 「V¹たつもりでV²する」 is an expression that means "do V² pretending / imagining / making believe / telling myself that I have done V¹".

Example:

「酒を飲んだつもりで献金します。」
"I'll donate the money, pretending that I have spent it on drinks."

特急 will help him arrive home faster, but more importantly it will not be too crowded and he'll get a seat. The sentence means "... I (often) end up riding it (paying ¥500), pretending I have spent the money for a cup of coffee."

Answer 2

For a train ticket 500 yens is quite expensive, but it is about the price of a coffee.

So he pays for the ticket, thinking "it is like buying a cup of coffee".