Hotseat may not be the best word, in fact, as Trevor - out of respect for Glenn - has not even used his small office, instead conducting meetings with the coaches in another room at the Chadwell Heath HQ.
West Ham United have had only nine managers in the club's 103-year history, and the last caretaker manager was, ironically, Glenn himself when he took the team to Middlesbrough in the final game of the 2000-01 season after Harry Redknapp had departed.
Ironic, then, that not only was Glenn taken ill following the Middlesbrough game this season, but we are now relying on Boro doing the Hammers a favour by getting a result at the Reebok Stadium on Sunday.
Trevor's remit ends when Sunday draws to a close, and he says: "'Privilege' is the word. I wouldn't have wished for the circumstances it came in, but it has raced by and been helped enormously by Glenn having done all the preparation for training and Paul Goddard and Roger Cross have carried it out.
"The players have responded and the fans have been great. There is support behind us and we have picked up six points.
"When it is all over you will be able to reflect a bit more but it is all a bit of a blur because it has gone past so quickly, but then Sunday will be upon us and it is done.
"The main thing is that Glenn is progressing and what, a couple of weeks ago, was a very uncertain time is a lot more happy from that point of view.
"And the club are at least, much as we desperately want to stay up, that much stronger together over the last couple of weeks."
Trevor has visited Glenn at home and he says: "He was fine, resting up, and hoping to get surgery next week. You feel then he will be making progress.
"He is home now and he just has to get stronger - and he is desperate for us to get three points as well and to finish on a high note.
"He has certainly followed the games and chuckled at one or two things that have developed - but he mustn't get too excited on Sunday.
"I am not sure I can tell him to do that, but he must remember not to get carried away.
"That will be difficult but it would certainly be a lot easier if we got our noses in front.
"He is very pleased and it has been a big boost to him that the run that he started has carried on with the last couple of wins and we are still in with a shout."