Toulon top the French domestic Top 14 league and have home advantage ahead of their quarter-final meeting.
However, Cockerill is hoping that his side can fully prepare for the conditions that they will face during the match.
"We are going there as underdogs and everybody is expecting us to lose," Cockerill told Sky Sports News. "They've got all the big-name players - or so they think - so we've got to prepare as well as we can and go there with a positive mind.
"We are going there a day early to acclimatise and look at the pitch and stadium. We're a little bit concerned that it's -2 degrees here all week and 20c on match day.
"It's a long and tough season. We have enjoyed getting to the quarter-final but we've got to put up a performance, and if we can do that there's a chance we can win. It's a big ask, but there's no reason why we can't do that."