If I'm sick, good luck getting anywhere near me, much less with a thermometer, rectal or otherwise. On a good day, I'm an asshole. On a day when I'm sick? Yeah, nah...it's not great. If I have a fever, I know about it because I feel like @#%^, and I'll go hide in a hole somewhere.
In ICU? Depends. MOSTLY, patients are monitored with standard monitoring protocols - in modern medicine, the question is basically "is there a fever or not" - it's ... binary. Which means an ear/forehead thermometer is as good as anything else - it can answer that question. Usually you are looking for fever in connection to something like infection. So you are rarely concerned with 'accuracy' of temperature, so much as you are with generalizations.
If you have one, a catheter with a temp probe is a god-send, since you don't need to do shit, you can simply chart from a walk-by of the patient's room. And in icu, you are much more likely to get this than in general. Absent that, however, temp is ... the same as anywhere else, it's a vital, and will be collected normally, but without any special consideration.