I have a forward primer with Tm 85 degree Celcius. I cannot change this primer. But I have two options for the reverse primer. One with Tm 65 degree Celcius (Annealing at 65 degree Celcius) and another with 72 degree Celcius (Annealing at 72 degree Celcius). First of all, will either of the primers work for me? If so, which pair would be better?
The default parameter provided by "primer-blast" is 3 degree (max difference between the melting temperatures of the pairs) . that said I think it really depends on the application. in case of cloning (in my experience) you can allow wider ranges of delta Tm between primers (in this case I used to use the average Tm of the two primers as annealing temperature). you accept to have a bad efficiency but eventually you can pull out your insert from the gel and clone it in a vector for a prep.
This really depends on your application, but from my experience 2-3 degrees with a max of 5°C difference usually works. The more the melting temperature differ, the more you need to optimize all the other parameters like salt and magnesium concentration, amount of enzyme, annealing and elongation times and so on.
85°C melting temperature seems very much for me, as you are 13°C over the optimal working temperature of the Taq polymerase. This willmost likely lead to a lot side products with incompletely bound primers. You can change the annealing temperature by shortening the 3' end of your primer (I assume that you need a specific starting point) so you get down at least a bit. Then I would probably order both other primers and test which ones works better, but I wouldn't expect that this works immediately and will need at least some optimization.
Can you give some more information why you can't use other primers and on your application?