Do you give blankets to febrile patients?

In my ER, you will be scolded by some older nurses and physicians if you bring blankets to someone with fever and chills who is begging for them. One nurse in particular is adamant that they receive only a sheet because she claims they will overheat.

I had a horrendous case of influenza last winter and I would have fought someone who refused me a blanket (I stayed home).

Thoughts?