Whilst I agree with what has been said, and that if it is not faulty then it is not the landlord's job to ensure the appliances are energy efficient, I would still mention it to the PM or landlord.
If I owned a place that had a continual turnover of tenants, and I was paying an agent a week's rent each six months or so and I found out they were leaving due to high heating or cooling bills, I would consider changing that appliance, especially if it is old.
I look at it similarly to an IP we had where the sewerage backed up into the yard every six months or so. After paying a plumber each time to run an eel through it, and knowing there were so many trees in neighbouring yards that we could never stop the roots from invading the old clay pipes, we bit the bullet and put in a new sewer. It cost about $4K from memory but our plan was to hold the house long term so money spent now saved us paying the plumber every few months and probably saved money in the long run.
Maybe the landlord has no idea why the tenants leave so often?