Manchester City goalkeeper Hart has found himself in the spotlight once again after the latest in a series of high-profile blunders which allowed Fernando Torres to fire Chelsea to a last-gasp 2-1 victory at Stamford Bridge last weekend.
However, amid speculation that manager Manuel Pellegrini is ready to drop the 26-year-old, he has received the backing of Tottenham counterpart Brad Friedel and now Clemence.
The former Liverpool and England number one told talkSPORT: "Joe Hart is the best goalkeeper England have got at this moment, but he is going through a difficult time, and I'm pretty sure he would be the first to admit that.
"It was interesting listening to Brad Friedel, and I agree with him. We all go through bad times and you need people to stand by you and have confidence in you.
"What we have to be careful of - and we are terrible for it in this country - is getting on somebody's back and destroying their confidence.
"I've seen it happen to Paul Robinson when that ball bounced over his foot in Croatia, and Scott Carson was never forgiven for the Croatia game at Wembley (where defeat for England cost them a place at Euro 2008).
"It just affects them and some don't recover from it. I don't want to see that happen to Joe. He's a wonderful lad, a great character and he has got a strong personality.
"They say as a goalkeeper you have to be daft but, at this particular time, you have to have thick skin because you are going to get more criticism than anyone else and you have to be able to rise above it."
Romania international Costel Pantilimon got the nod for Wednesday night's 2-0 extra-time victory at Newcastle in the Capital One Cup, and Clemence believes the competition he provides could prove key.
He said: "It's good to have somebody that makes you think, 'If I make a mistake here, I'm under pressure and I might not be in the team next time'. Intense competition does keep you on your toes.
"At Liverpool, they used to change the reserve goalkeeper every three years to make sure I had a new challenger so I didn't get complacent.
"It does help, without a shadow of a doubt. John Ruddy and Fraser Forster have come a long way in these last few years and are doing really well themselves and putting pressure on him (with England). Ben Foster, when he gets fit again, will put pressure on Joe as well."
Alex McLeish, who took Hart to Birmingham on loan from Manchester City for the 2009-10 season, is certain his former charge will overcome the slump in form.
But the former Scotland boss also thinks England manager Roy Hodgson would have to think twice about selecting Hart if he became second choice for his club.
"Certainly Roy, in a team such as England's magnitude in world football, they wouldn't go - I don't think they would go - with a goalkeeper who's been out of his club football for a long period of time," McLeish said on Sky Sports News.
"I do believe that Joe will get over this.
"As Ray Clemence said, we don't know what's going to happen tomorrow. Speculation is that Pellegrini might leave him out.
"Pantilimon did really well the other night, made a great point-blank save at nil-nil, took cross balls well, but I'm sure Joe will be bursting just to show everybody he can do it. Whether he gets a reprieve from Pellegrini remains to be seen."
Everton manager Roberto Martinez said he believed any move by Pellegrini to drop Hart would come from a desire to protect the goalkeeper.
"Joe Hart is a fantastic goalkeeper but every player in the world goes through good moments and bad moments of football", Martinez said on Radio Five Live.
"The manager can protect the player. But it's not just about dropping him, it's also about giving the opportunity to another player and helping Hart get back to his best."
Martinez was critical of the swirl of attention which has followed Hart in recent weeks, arguing matters had been taken out of proportion.
"It's been a little bit unfair in terms of the surroundings to his performances," he added. "Every single action by Joe has been analysed and that's sometimes a little bit unfair. It can affect your performances.
"Pellegrini is protecting Joe Hart. He's taking him out of the firing line. It's unfair Joe is under so much scrutiny".