A 2-0 defeat by Hearts in November, in what was Robbie Neilson’s last match in charge of the Jambos before Ian Cathro took over as head coach, saw the home side leapfrog the Ibrox club into second place in the Ladbrokes Premiership.
The Light Blues rallied and have lost only once in eight games since - to rivals Celtic - to regain second spot behind the Parkhead club, who are runaway league leaders.
Warburton, whose side won 2-0 win against Motherwell at Fir Park on Saturday, put their last Tynecastle trip down “a bad day at the office” as he looks to continue their good form.
He said: “We said straight away ‘ no excuses’. The important thing was how we responded and we responded outstandingly well, beating Aberdeen, beating Hearts etc with very good performances and a good run of games.
“We go in to the game on the back of a very good performance (at Motherwell), second-half especially, and we have to take that belief into the game, recognise the challenge and deliver the performance.
“We are getting towards the business end of the season and we have to keep on pushing forward.”
Warburton knows it could be a vastly different Hearts side to the one which hosted the Gers in November as Cathro has brought in nine new players during January.
He said: “We are not sure what team we face.
“But we know they will be well organised by Ian and Austin (McPhee, assistant) and we have to expect a very tough challenge.
“But it is about us, if we can go there and deliver a performance we will be fine.”