The literal translations and the meanings are:
- Am Samstag sollten es über dreißig Grad werden.
On Saturday it should become over thirty degree.
On Saturday the temperature should rise above thirty degree celsius.
The focus is on the fact that the temperature will change. It's the transition from the actual temperature to the future temperature that we're talking about. The verb sollten is in plural, because we are talking about 30 degrees.
- Am Samstag sollten es über dreißig Grad sein.
On Saturday it should be over thirty degree.
On Saturday the temperature should be above thirty degree celsius.
Here the focus is on the fact that the temperature will be at a certain level. We do not talk about what was before. We talk about a state. And again: The verb is in plural for the same reason as before.
- Am Samstag sollte es über dreißig Grad haben.
On Saturday it should have over thirty degree.
On Saturday the air (everthing outside) should have (a temperature of) more than thirty degree celsius.
This sentence is like #2, but here we do not talk about the abstract concept of "temperature" that will reach a certain level. In 3 you talk about how worm the air will be (or something else that is outside). We are not talking directly about a physical quantity, we talk about a thing that we can feel. And for this reason the verb is in singular, because it no longer refers to the 30 degrees but to the air, and there is only one air.
In German you can say
Das Wasser im Pool hat eine Temperatur von 23 Grad.
The water in the pool has a temperature of 23 degree celsius.
But it is more common to say just
Das Wasser im Pool hat 23 Grad.
The water in the pool has 23 degree celsius.
So,
Heute hat es 23 Grad. (Präsens)
Morgen wird es 23 Grad haben. (Futur I)
means
Today's temperature is 23 degree celsius.
Tomorrow's temperature will be 23 degree celsius.
You don't say (this is wrong)
Heute ist es 23 Grad.
Morgen wird es 23 Grad sein.
But you can say (this is correct)
Heute ist es 23 Grad warm.
Morgen wird es 23 Grad warm sein.