Can one put aside for this purpose, can one open a bank account in the Bais hamikdash’s name, knowing that it will be rebuilt , using the Har Habayis as real estate asset?
It is nice that you have such feelings for the Bais Hamikdash, but it is not something that I would recommend. The first reason is that the third Bais Hamikdash will come down whole from heaven, and Hashem is the one who is going to build it, therefore donations for it will not be needed. Secondly, if you say that certain money should go for the Bais Hamikdash, it might make the money “hekdish”, and it would be a sin to benefit from that money, and having such money around can cause you all sorts of issues.
There is another option. The Midrash says that the shuls nowadays are considered miniature Bais Hamikdash. Therefore in essence when you donate money to the building of a shul it is like you donated money to our nowadays Bais Hamikdash. Of course until the real one will be built, which we all pray should happen soon.