Unfortunately, its because of the Exynos 990 chipset inaide the S20 FE 4G variant that causes battery drain. If the phone is still within the return time the return it asap and either buy the S20 FE 4G with the Snapdragon Chipset or the S20 FE 5G.
You maybe unlucky Members_FRR9Sel and have bought a defective handset. If your Wife's phone is brand new or this problem has suddenly occurred after a recent software update then there is hope it may settle down in a few weeks but if it has been going on for more than a couple of months you may need to consider a replacement phone. I don't think the problem is purely to do with the Exynos 990 chipset as I have been on some forums where I have seen reports of the Snapdragon 865 chipped S20 FE's having the same battery drain and overheating problems, so I would suspect a software issue could be at play also. This said and in balance I would echo APAMAR's advice and still advise you to go for the Snapdragon chipped version if it is the S20 FE 4G you really want as they have not been affected in the same number as the Exynos version so there is less chance of your Wife getting a dud phone again. All the best of luck to you and I hope your Wife ends up with a cool running long lasting phone in no time. 👍👍