I'm not describing any equilibrium. Heat deaths and cold deaths move in opposite directions, but that does not imply that they are equal or produce any restorative force on one another that would lead back to an equilibrium state. Since death won't affect the weather, if temperatures change, both heat and cold deaths will change, with some net change in total deaths.

With more cold deaths currently than heat deaths, an increase in average temperature is more likely to reduce total deaths than increase them. If saving lives is your real goal, net lives saved/lost should be your yardstick, regardless of your opinion about the relative magnitude of heat deaths and cold deaths. But if your real agenda is something else then, sure, talking about increased heat deaths without ever mentioning reduced cold deaths might better serve your needs.