How about Georgia, Armenia and Azerbaijan. Pretty close to Bulgaria. I lived in Tbilisi for 6 months. Well worth a visit.
Panama is not particularly hot at any time of year (usually below 90 F). Not much in the way of museums, but as for history we have Old Panama (burned in the course of being sacked by the pirate Henry Morgan), the fortress of Portobelo (Sir Francis Drake is buried somewhere off shore, after his death while planning an attack) and a number of other sites associated with pirates, the Spanish Main, and the gold trail of El Camino Real. Not to mention the Panama Canal.
Colibrí - in my experience, Panama is very hot and humid in summer, even in comparison to the Dominican Republic which is bad enough. It is a gorgeous country with plenty to see and do, though.
Any of the highland towns and cities in Central or South America claim to enjoy ‘eternal spring’ weather - there are many including Antigua (Guatemala), Copán (Honduras), San José (Costa Rica) Quito (Ecuador), Cuzco (Peru) - all good choices.
If it is hot though, as it was when I was there in the (northern) summer a few years ago, it’s very unpleasant. The older style hotel in which I was staying had no airconditioning.