No, because starting a war over this would be ridiculous and stupid.
I would supporting possibly suspending relations with a country or recalling an ambassador for consultations, though, depending on the situation.
I believe arresting a country's former president for the things he did while he was in office is like an attack on that country. Maybe its not an all out war but maybe a minor one like attacking the country who arrested your former president interests to weaken them internally and externally . If a country arrested a US president , I believe this is what we should do ,
1. Cut of all ties with them and sanction them
2. Try to weaken their political stability
3. Try to weaken their economic stability
4. Tell their enemies that we will not defend them if they decide to go to war with that country
If you do these things none of these threats to arrest a former US president will ever happen, and that president would be free to travel anywhere he wants .