damper open for summer ops?

Hi Guys

My boiler room gets pretty warm and as the outside temps go up and I'm worried that my house will be too warm.  My cast iron boiler has an automatic vent damper that can be set to stay open.  Would it be good to leave it open for the summer since it still provides DHW?

Are there any disadvantages to this aside from a little waste heat going up the chimney?

Thanks

Derek