Right, I'll try the shower thing! Very entertaining for my guys at home

I should have been a bit more specific in my question. I meant - is it really any warmer to wear a full top than a bra, when they're soaking wet?

Normally a shortsleeved or sleeveless top is what I'd wear to bike or run at those temps, about 17-18 C/ 62-64 F, a little wind, sprinkling of rain. But I felt colder than I'd expected because of the wet material. So I'm thinking I'd should go for just a bra, and put on a dry layer if I'm worried about getting too cold.