It is not true, and I shall provide the explanation - physics style.
There is a myth that a bigger heatsink dumps heat faster to the surrounding hence heats the surrounding up.
While that is true if talking about lower thermal resistance...
But understand where the heat is coming from.
All of the heat energy is coming from the graphics card.
And all this heat energy will have to be dissipated to the surrounding.
Regardless of the size of the heatsinki.e. rate of heat transfer is constant (to be precise, when the graphics card temperature stabilizes)
A smaller heatsink just means a higher temperature before this amount of heat transfer takes place - since rate of heat transfer is dependent on temperature difference between the two.
To illustrate, an example -
A 50W gfx card, a 1°C/W lousy heatsink, and a 0.5°C/W decent heatsink (in comparison, good CPU coolers are 0.25°C/W and lower), with air temperature at 30°C constant.
The same 50W gfx card will reach 50W x 1°C/W + 30°C = 80°C on the lousy heatsink, and 50W x 1°C/W + 30°C = 55°C on the decent heatsink.
But both will dump 50W of heat into the surrounding. Just at different temperatures.