A final score of 0-0 was the only possible outcome of a game that was played between two supremely-powerful teams, both of whom harbour ambitions of a top seven finish come the season's end in May.
Upon Thompson's arrival, the new Magpies manager had outlined his plan to play on-the-grass football in a 4-4-2 formation featuring pacy wide players in David Pipe and Andy Parkinson.
And, after the season's opening day draw at Lincoln City, few would have doubted him. Both wide players were integral in an exciting new side that looked as though it had the potential and vibrancy to improve.
Five league games in, Thompson has made an undoubtedly impressive start. And today's match proved that they were able to stand-up to one of the most physically strong teams of this or any other season.
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The Magpies fought fire-with-fire, and it made for a dreadful game to watch.
All the talk prior to the fixture had been of a war-of-words between the two managers, Thompson and Keith Alexander.
Thompson had labelled Alexander's Posh outfit a long ball team. Alexander had countered that Notts too were a direct side, relying on the aerial presence of Jason Lee in attack.
After today's 90 minutes, few would argue with either man's assessment.
Nottingham-born Alexander is a man with a reputation at this level, after four successive top-seven finishes at the helm of Lincoln City.
Playing his trademark 3-4-3 system, Alexander brought a Peterborough team to Meadow Lane more bigger and more brutal than any one of his Lincoln side's.
While familar faces Richard Butcher, Simon Yeo and - on the bench - Ben Futcher were remaining from his Imps days, the likes of Trevor Benjamin, Guy Branston and Justin Richards have provided additional man-mountains that are tailor-made for Alexander's infamous style of play.
Even Notts' new hardmen Alan White and Matt Somner were dwarfed by this trio of Giants, with Lee's battle with Branston providing particular interest.
By the end of a first half devoid of any goal attempts, both players had been booked and it seemed almost-certain that at least one would be given their marching orders under the shaky stewardship of match official Graham Hegley.
Hegley, a youthful man who was clearly lacking in first-class experience, wasn't ready to be awarded such a match that was obviously going to be of a physical nature.
Twice the Posh players called for Lee to be sent-off after visiting defenders were sent to the sidelines with facial wounds.
Not that anyone could accuse the novice official of being one-sided. His worst call was his failure to give the home side a penalty when Lee was blatantly pushed by Branston when attempting to get on the end of a floated free-kick.
The match official's inexperience was also in evidence at set-pieces when multiple pushing and grappling was allowed on either side.
With football at a premium, Notts were only able to create one noteworthy goal chance in either half.
In the first, Lee headed wide after excellent work from Junior Mendes. Mendes himself was the culprit with the Magpies' other effort, seeing his volley well-parried by Mark Tyler when faced one-on-one with the long-serving stopper.
Though Alexander himself was more pre-occupied with bickering with the home support in the Main Stand over his style of play, his team also came close to snatching a late underserved winner in-front of their excellently-sized travelling fans.
Branston - the villian for Notts fans - was the man to come closest, heading narrowly wide from an almighty long throw.
Benjamin was the other culprit, the much-travelled striker missing from a tight angle after rounding Kevin Pilkington.
But this wasn't a day for the football. This wasn't a day for the purists and this certainly wasn't a day for the paying supporter.
Thompson though, will be fairly content. Greeted with contempt upon his arrival, the Notts manager is still yet to lose and provided much amusement to supporters due to his verbal bashing of his opposite number.
There may still be much work to do, but, on the day when the Magpies were faced with yet another trip to Premiership Middlesborough in the Carling Cup, a point against a promotion-chasing outfit should be viewed as a positive.
Entertaining, or not.