I would like to enter into negotiations with the heating engineer and confront him with it.
... and the heating engineer will then tell you that you are welcome to buy at the low prices online. But then you have to install it yourself and give yourself the warranty for it. By the way, this price issue will come up throughout the entire house construction. Ordering windows from Poland is cheaper than from the German window maker. Insulation materials on the internet are also cheaper. Etc. Do you approach every trade and say, "But I can buy cheaper than you!"? Compare craftsmen with each other, but not the pure purchase prices. A craftsman does not only have material costs. He has hourly wages, vehicles, office employees, office space, storage/production rooms, insurance, etc. All that has to be paid for. And he buys from wholesalers, not from some internet shop. The wholesaler is not cheaper just because it is called a wholesaler. For example, go to Metro and find items that are cheaper than at regular grocers. I also calmly bought my two heat pumps on the internet. However, I also took over the entire heating installation myself (including underfloor heating). But for that, I can't just call a plumber to please fix what he messed up.