The Asepsis 1-4 videos in the CPNE Online Workshop goes into detail regarding this topic....
The answer depends whether on the situation... if you are in the isolation room, your gloves and gown should never come off when in contact with the patient. You may not have access to your PCS Response Form if it in your coat pocket under the gown. I'm an epidemiologist by training so I will make you a little more paranoid than needed. In this case. I will record vitals on a piece of paper.. after vitals go away from the patient to the sink. Change gloves (clean between gloving of course), write them on my PCS Response Form before I come back to the patient for anything else.
If it is not an isolation patient, with intact skin, usually there is not much of concern. If you are wearing gloves for vitals anyway because you don't like touching anyone without gloves. I would do the same... separate piece of paper, take gloves off, wash hands, transcribe vitals
Most of the students are just writing vitals as they go along on their grid and later transcribe it in the PCS Recording form before they "Declare" them. I would take the temp last (especially oral). Take my gloves off, wash hands, then write the temp in just in case my gloves are contaminated.