i've seen threads talking about the heat issue of it, and seems like giving it a heat shrink is a good idea

However I'm thinking if I supply the lowest voltage it can take, will the heat issue be reduced with same output power?

it gets really hot when i give 12V to it

Oscar has an article on reducing heat on this VTx here: https://oscarliang.com/fix-overheat-issu...ansmitter/

Any video transmitter can get hot, it's a normal behavior, just make sure you don't power it on too long sitting on the ground. With good airflow during flight it should be fine.

Heat shrink doesn't help with overheating, i guess you mean heat sink. Yes it might help reduce the heat.
Also feeding VTX can help too since it reduce the heat from voltage regulator.

see my post: https://oscarliang.com/fix-overheat-issu...ansmitter/

I had used the same vtx for a while and was worried about the heat but in flight with airflow makes a huge difference to cooling, the vtx lasted me a good while too

Using a FLIR or temp ir cam, Has anyone ever posted pics of the heat in a transmitter like the ts5828 in its first 2 minutes. It seems after 4 years the ts5828 still can overheat and shuts down after 3 minutes.
I have 4 of them and 1 shuts down. the others get too hot to touch.