Strong exothermic mixing of two 'safe' liquids
If you need a quick source of moderate heat, why not use a single liquid? Sodium acetate trihydrate ($\ce{CH3COONa·3H2O}$), for example, releases heat energy on crystallization... and it takes very little to trigger that crystallization! Commercial heat packs contain a "clicker", which makes a sharp vibration. You can make your own heat pack fairly safely and inexpensively: sodium acetate can be found for ~US$8/450 g, and a Safety Data Sheet states, "it's  not classified for physical or health hazards under GHS."

Not only can you get a noticeable temperature rise quickly, it's reusable.

It would be more difficult to find liquids that quickly release energy that do not have physical hazards (e.g. ignition) or health hazards. Hypergolic fuels, for example, tend to be rather toxic, as well as explosive. You might get a bang out of reading John Drury Clark's Ignition!, though.