The Blues host already-eliminated Parisians Racing Metro in Pool Two, while Edinburgh entertain London Irish with Cardiff and their Scottish rivals currently tied on 17 points.
Warburton and company could be out of the competition by Sunday evening, celebrating a Heineken quarter-final spot or even finding themselves in the second-tier Amlin Challenge Cup knockout phase.
The Blues, though, are in control of their own destiny to the degree that a bonus-point victory at Cardiff City Stadium would guarantee they progress as group winners.
"It's going to be a funny one in that we will have to give it our all, but we perhaps won't know until the final whistle if it is good enough or not," Blues flanker Warburton said.
"All we can do is focus on ourselves and do everything we can to make sure we get that win.
"Normally, teams would think they could well be in the quarter-finals with four wins at this stage, but it has been a tough group and Edinburgh are pushing us all the way.
"I don't think a lot of people expected this scenario, especially Racing having three home defeats.
"It is very tough to go to France and win, but that has opened the group right up and Edinburgh will throw everything at Irish, so it is going to be a really close one to call.
"Getting a home semi-final is a huge incentive. If we could get five wins I think we probably would be one of the top four qualifiers, and a home quarter-final draw would be fantastic.
"I was up in the stand for that semi-final in 2009 when more than 44,000 turned up for that Leicester game at the Millennium Stadium.
"That is the sort of game in which you want to be involved, and in the last two years we haven't quite been there. You really want to win the big one, and that is the Heineken Cup."
The Blues are again without Wales centre Jamie Roberts, who is recovering from a knee injury, while Gavin Henson has been replaced by Gavin Evans alongside Casey Laulala in midfield.
Reigning Aviva Premiership champions Saracens need a point from their appointment with Treviso in Italy on Sunday to win Pool Five, and they are likely to carry a lone English flag in the last-eight following Harlequins' 9-8 defeat against Connacht on Friday night.
Victory for Saracens would mean home advantage in the quarter-finals, although rugby director Mark McCall said: "We are not quite there yet, and that will focus our minds as we head out to Italy.
"There is still a lot that can happen in this group, but we've just got to take care of our own business and that means getting the job done against a good and organised Treviso team."
Elsewhere in Pool Five, Biarritz and Ospreys clash at Stade Aguilera. The winners are probably destined for an Amlin spot, with Heineken progress a distant possibility.
"It is a big challenge that we face, but we know what we've got to do. There is no margin for error on Sunday," Ospreys coaching director Scott Johnson said.
"Biarritz is always a difficult place to go. Any French club is the same, particularly when we are in a straight shoot-out for a qualification place."
In the Amlin tournament on Sunday, Wasps can temporarily put their Premiership struggles to one side by securing a last-eight place courtesy of defeating Adams Park visitors Bordeaux-Begles.
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