The visitors resumed on 125-1 and batted through the day to make 335-7. They declared and with no chance of a result, the game was drawn.
Warwicks picked up twelve bonus points with Middlesex eight.
The Bears face Ireland tomorrow in a Friends Provident game at Edgbaston. They go into the game without Darren Maddy who will be out for six weeks with a broken hand.
Their final FP game is against Leicestershire at Oakham School on Monday. Play for both matches starts at 12 noon.
In the Test Match at Old Trafford, New Zealand declared on 381-9. England went into bat and were 81-1 after 33 overs.