Almost certainly not. There's been more recent studies on cold water immersion that basically say it's useless for something but I can't recall the specifics of what in particular they were studying. You'll have to google it. Also, a shower isn't going to have the cooling effect an ice bath will so any effect of ice baths is likely to be much less for a cold shower. Basically, worry about your gym work, not the temp of your shower.
Almost certainly not. There's been more recent studies on cold water immersion that basically say it's useless for something but I can't recall the specifics of what in particular they were studying. You'll have to google it. Also, a shower isn't going to have the cooling effect an ice bath will so any effect of ice baths is likely to be much less for a cold shower. Basically, worry about your gym work, not the temp of your shower.