Yes, travel insurance is worth carrying for a trip to Thessaloniki, even though Greece has solid hospital care and EU or UK visitors have some baseline protection through reciprocal health arrangements. The honest reason to add a policy is what those arrangements do not cover - trip cancellation, delayed baggage, and gaps for anyone outside those specific reciprocal schemes.
Whether your own health cover extends to Greece depends entirely on your country of residence and specific plan, and this page cannot determine that for you; EU and UK travelers should check their own EHIC or GHIC entitlement, and everyone else should check whether an existing health plan extends abroad and specifically to Greece before assuming it does. A standalone travel policy remains the simpler, more complete option for most visitors regardless of what a reciprocal scheme technically includes.
Thessaloniki itself has good city hospital care, and most visitors use it as a base before heading onward to Halkidiki, the three-pronged peninsula east of the city known for its beaches and resort towns; that onward leg brings ordinary coastal-travel considerations rather than any unusual risk. Summer, roughly June through August, brings genuinely intense heat across northern Greece, and heat-related illness is a real concern for visitors unused to it, particularly around midday activity in the city or on the coast.
Keep any clinic paperwork and receipts if you need treatment, since Greek providers, like most in the EU, generally issue standard invoices on request. Check your policy's documentation requirements before relying on memory later, and confirm whether non-emergency treatment needs pre-approval under your plan. Trip-delay cover is worth checking if your visit depends on tight connections between the city and Halkidiki resorts during the busy summer season, when transport and accommodation both run close to full capacity across the wider region.