Have you made a proper contract with the construction company? If yes, then have you inserted a clause on the delay or deficiency in services? If this clause is not inserted or if the contract itself is not made, then serving a warning letter to the contractor will become inconsequential.
Delay in the completion of work by interior designing companies or construction companies is quite common. Therefore, some delay is condonable.
In view of this, I recommend you write the warning letter on your own and upload it here. Someone senior like me will correct it.
Thanks,
Dinesh Divekar