Rug is bang on the money,
I also use Uniqlo Airism t-shirts underneath my white shirt.
Inexpensive, good quality and do a damn good job.
Regardless, some people sweat more than others when it comes to heat and humidity. And if you're inclined to sweat more, there is not much you can do about it.
But a decent undershirt likes these uniqlo's helps make a difference.
But don't get an undershirt that is too tight....get one size up is my 2 cents.