The omens did not appear bright in the build-up to this game against fellow strugglers Luton Town as the Sky Blues played at home for the first time since Micky Adams was sacked a fortnight ago.
With leading scorer Stern John sold earlier this week to Sunderland and captain Robert Page and Michael Doyle deemed not in the right state of mind to play following last week's training ground bust-up, Heath looked to his players to give the club a much-needed pick-me-up.
Instead a desperately poor first half was served up for their long-suffering fans as neither keeper was fully tested in an awful advert for Championship football.
Luton, who were decimated by injuries, created the first chance within the opening minute. Sol Davis lofted a free-kick from the halfway line into the box, and when Andrew Whing failed to cut out the danger, striker Dean Morgan sent a shot from an acute angle flashing wide of the far post.
David McNamee attempted to inject some life into the home team's play when he ran half the length of the field only to be crowded out by defenders as his shot from the edge of the area was blocked.
At the other end Colin Hawkins - returning to the club he left a decade ago - was able to monitor Morgan without too much fuss.
Whing's long punt was headed back towards keeper Dean Brill by defender Keith Keane and Dele Adebola latched onto the ball but the 21-year-old was alert to the danger.
After the break, the Sky Blues went in search of a breakthrough when Chris Birchall's 46th minute strike was blocked.
The tempo of the game remained downbeat although the home team did finally to start to show some attacking instincts.
Adebola released strike partner Michael Mifsud and when he exchanged passes with captain Stephen Hughes, the Maltese striker fired in a low 15-yard shot wide of a post.
Heath threw on Kevin Kyle and Leon McKenzie in the 63rd minute for Birchall and Adebola and Kevin Thornton followed for Isaac Osbourne nine minutes later as the home team tried desperately to find a way past Luton.
Mike Newell's men had a chance when Lewis Emanuel's cross was headed over the bar by new signing Matthew Spring on his return to the club he left for Leeds.
The breakthrough finally came in the 76th minute. Thornton's pass reached McKenzie inside the box and his 10-yard shot took a deflection off defender Russ Perrett to deceive the keeper and land in the net for his fifth goal of the season.