ApE (A plasmid editor) is able to predict a temperature (Tm) for a given sequence. I usually take this value as annealing temperature in my PCR and it is almost always working very well.
As you see there are a lot of options to calculate Tm. Even primer blast gives you a Tm. However, you must keep in mind all of them are just predictions and you need to do the experiment to really now it.
People usually recommend to start with a Tm a couple of ºC below the calculated Tm.
There are multiple factors that effect the annealing temperature of primers in PCR. It is primarily dependent on the Tm of Primers. Primer Tm can be calculated using any of the multiple tools available on the internet. The annealing temperature is usually taken as 5ºC below the Tm of the lower Tm primer. However, it also depends on the Polymerase enzyme and buffer system that you use. The tools by Thermofisher and NEB allow calculation of the Annealing Temperature according to the enzyme and buffer to be used. Additionally, if the PCR reaction requires addition of DMSO, the annealing temperature will reduce.
Moreover, the best annealing temperature for your set of primers can also be optimised by PCR using a Temperature Gradient.
OligoAnalyzer 3.1 is a primer analysing tool from integrated DNA technologies. You can use below-given link to check your primer Tm, Hairpin, Self-Dimer, Hetero-Dimer and Tm-Mismatch.
You may use any of the programs available, but may also run some systematic tests with different temperatures - especially higher temperatures to increase and optimize the specificity.