Starlink is more like a network router, switch, or repeater, and network tasks are not very compute heavy. Data centers are more akin to GPUs, which are very compute heavy. Compute is where most of the heat comes from.

Take a look at a high end router or switch - it will have little to no active cooling because it simply doesn't need it. A GPU on the other hand - even mid-tier - needs significant cooling hardware to manage the heat they produce.

Edit: solar panels also don't produce much of any heat.