We always ask our patients whether they'd like to lay flat or have the table in a more upright position. Various women prefer one or the other. Tell your doctor that you have some issues of couging while laying down, and would like the table to be more upright so your upper body can be upright. There is NO reason why they can't do it like that.
Also, YES, as them to warm it up a bit. I always do this for my patients, even if the MALE doctors tell me it's not necessary. I kindly remind them afterwards what it would be like to spread their A*sh*le and for me to shove a freezing duck beak in there, wouldn't they rather have it warm?