It is now rather uncommon for the heating engineer to also design the insulation. It is of course clear that this takes longer. That it naturally requires 1 week is too much. Realistically, 2 to 2.5 days would be more appropriate for a "precise" design.
The question remains, of course, why the architect handed over the design to the heating engineer! From an outsider’s perspective, you had a fixed price with the screed layer and now the insulation design is charged at an hourly rate by the heating engineer. Since the architect told you this and you agreed, the contract is also verbally valid.
The only thing you might still try is to have the work hour records shown/given to you. These should include the date, employee, time, and materials used. They should be signed either by the client (you) or the architect. Whether this is legally binding in case of dispute, I cannot tell you.
Best regards