Actually in vampire lore - seeing it is all we have to go by anyway - Vampire do not supposedly feel heat or cold. It is the sunlight itself that is their enemy and technically even sunscreen would not separate them from the deadliness to them the sun is. But in vampire lore they generally dress appropriate according to the seasons so as not to stand out but they do always stay in the shadows in someway when the sun is out as it is considered in some lore deadly to them and in twilight to make them sparkle apparently - the sparkle would of course make them stand out and noticeable by the non-sparkling living humans. LOL. - which in it's own way would be "deadly" for them as well.
So anything that kept them in the shadows and would not draw attention to them being different than living humans would be a plus. A sun parasol is a very good idea.