Quantum computation requires many qubits that can be coherently controlled and coupled to each other1. Qubits that are defined using lithographic techniques have been suggested to enable the development of scalable quantum systems because they can be implemented using semiconductor fabrication technology2-5. However, leading solid-state approaches function only at temperatures below 100 millikelvin, where cooling power is extremely limited, and this severely affects the prospects of practical quantum computation. Recent studies of electron spins in silicon have made progress towards a platform that can be operated at higher temperatures by demonstrating long spin lifetimes6, gate-based spin readout7 and coherent single-spin control8. However, a high-temperature two-qubit logic gate has not yet been demonstrated. Here we show that silicon quantum dots can have sufficient thermal robustness to enable the execution of a universal gate set at temperatures greater than one kelvin. We obtain single-qubit control via electron spin resonance and readout using Pauli spin blockade. In addition, we show individual coherent control of two qubits and measure single-qubit fidelities of up to 99.3 per cent. We demonstrate the tunability of the exchange interaction between the two spins from 0.5 to 18 megahertz and use it to execute coherent two-qubit controlled rotations. The demonstration of 'hot' and universal quantum logic in a semiconductor platform paves the way for quantum integrated circuits that host both the quantum hardware and its control circuitry on the same chip, providing a scalable approach towards practical quantum information processing.