Hello Junus2012,
If I understand correctly you are talking about systematic offset (not offset generated by mismatch variations).
Anyway yes, temperature depended offset drift is a know phenomenon, existent in all the opamps, and what you see with your simulations, under open loop conditions, is perfectly normal. Since we are talking about systematic offset, what happens is that simply the transistors have slightly different operating points that set the output node to a different voltage. You should check if all your transistors are in the expected region of operation, probably saturation.
A better way to determine if your design will work or not is Monte Carlo simulation.
The equivalent of corners is Monte Carlo with the "process" option checked ("mismatch" unchecked).
Now, If for example 99 out of 100 sims show that your circuit works correctly then it is ok! (I don't know about the industry's standards, but for academia this circuit is golden!)
On the other hand, I guess you will not be using your opamp in open loop configuration, and shouldn't be running open loop simulations.
You can set your opamp in a unity feedback loop and use either the sp1tswitch in analogLib, or the large RC method to break the loop under AC only.
Alternatively you can use iprobe and stb analysis.
I bet that your circuit will now work as expected.