OK, you got my burner goin'...
The worrisome flatmate is correct that -- if you take the view of considering the time the heat is enjoyed (ie, briefly before going to work) -- it is more costly *per minute of enjoyed benefit* from the fuel used to heat the flat. But the cost of that fuel used to heat for that 10 minutes isn't any more costly than that same 10 minutes when they get home in the evening. Except... Because it is, presumably, colder in the a.m. than in the p.m., it may require a *little* more fuel to heat the flat to 24o C in the morning, but as Sue said, it doesn't amount to much more "scratch".
The heat isn't "more costly", but without anyone there to enjoy it after you've both gone to work, maybe that's what he means by "costly": a few pence for only a few minutes of warmth, whereas if it was evening, someone might enjoy that comfort for an hour.
My read is that the flatmate is saying, in essence, "Suck it up, matey. It's such a small period of time to be cold before getting into your car (which can be heated with waste heat from the burning of fuel -- basically, "free") or arriving at work where *they* pay for your comfort".