Bargoed have already accounted for BP Llandarcy (37-6) and Pill Harriers (23-20) away from home in the cup this season and their reward is a plum home tie at The Park against the seven times winners.
'This is the first time we have ever met Cardiff and we are in good form having gone 35 league games without defeat,' said Bargoed secretary Robert Butcher. 'I skippered the side that played Newbridge in 1977 when we lost at home by two penalties to nil, and since then we have entertained Llanelli and Cross Keys. We even led the Scarlets at half-time.
'Our support was good then and still is. Glen Seabourne, our captain, and our coaches Stephen Barber and David Lynch all have a lot of experience. Our pack is solid and I think we will give them a good game.
'It is a great draw for us. I'd love to be playing in a game of this stature, but I'm 20 years too old these days.
'There is no thought of us moving the game to another venue - The Park will be full and it is going to be one of those very special Konica Minolta Cup occasions.'
The one consolation from the draw for Cardiff is that if they win they will have home advantage in Round Four against the winners of the other tie in Group 15 - Bonymaen or Bryncoch.
While Cardiff will be hoping to carry the Premiership flag into the next round - the third round draw was done in groups of four clubs so the winners will know who they meet in Round Four - there will be at least one casualty from the top division.
Near neighbours Llanharan and Bridgend have been drawn against each other in Group 16 and will do battle at the Dairy Field for the second time this season.
When the newly promoted Llanharan hosted their close rivals in the Premier Division in September they beat them 24-23.
The Konica Minolta Cup holders Neath begin their defence at home to Penallta, who are in their first season as a Welsh Rugby Union club. They have made a fine start to their WRU career, scoring 155 points in three cup matches to date ro reach Round 3.
Newport entertain Abercynon, who will remember with pride their 14-3 loss at Rodney Parade in the 1977-78 competition, while veteran Dunvant forward Paul Morris will be pleased to be going back to his old club, Llanelli, at Stradey Park.
Beddau player-coach Brett Davey will be hoping his club can win at Tenby and possibly draw one of his former clubs, Caerphilly, at home in the next round. Two Division One clubs clash at Llynfi Road, where Maesteg entertain Llangennech.
Maesteg have already beaten the west Wales club 34-20 in the league this season. Victory for either club could mean a trip to Swansea in the next round.
Konica Minolta Cup Third Round Draw
Matches to be played on the weekend of 18 December 2004. Winners of the first match in each group will be at home to the winners of the second match in Round Four.
Group 01 - Tonmawr v Cwmllynfell
Crymych v Bedwas
Group 02 - Senghenydd v Banwen
Builth Wells v Newbridge
Group 03 - Neath v Penallta
Pembroke Dock Quins v Penclawdd
Group 04 - Pontycymmer v Llantwit Major
Newport v Abercynon
Group 05 - Tredegar Ironsides v Carmarthen Quins
Maesteg Quins v Pontyberem
Group 06 - Swansea v Treherbert
Maesteg v Llangennech
Group 07 - Bedlinog v Fleur de Lys
Llanelli v Dunvant
Group 08 - Talywain v Llandovery
Llantwit Fardre v Ynysybwl
Group 09 - Pontypool v Kidwelly
Tonyrefail v Merthyr
Group 10 - Tenby Utd v Beddau
Caerphilly v Mumbles
Group 11 - Vardre v Skewen
Narberth v Aberavon
Group 12 - Whitland v Aberdare
Blackwood v Pontypridd
Group 13 - Carmarthen Ath v Cwmbran
Ebbw Vale v Glamorgan Wanderers
Group 14 - Cross Keys v Blaina
Rumney v UWIC
Group 15 - Bargoed v Cardiff
Bonymaen v Bryncoch
Group 16 - Llanharan v Bridgend
Mountain Ash v Abercwmboi