```ts
export function runThermostat(start: number, low: number, high: number, power: number, drifts: number[]): { temp: number; heated: number; switches: number; coldest: number } {
    if (!Number.isInteger(start) || !Number.isInteger(low) || !Number.isInteger(high)) throw new Error('Start, low, and high must be integers');
    if (low >= high) throw new Error('Low must be strictly below high');
    if (!Number.isInteger(power) || power <= 0) throw new Error('Power must be a positive integer');
    if (!Array.isArray(drifts)) throw new Error('Drifts must be an array');
    if (drifts.some(d => !Number.isInteger(d))) throw new Error('All drift values must be integers');

    let temp = start;
    let heated = 0;
    let switches = 0;
    let coldest = start;

    for (const drift of drifts) {
        const heaterOn = temp < low || temp >= high;
        if (heaterOn) heated++;
        if (temp < coldest) coldest = temp;
        temp += drift + (heaterOn ? power : 0);
    }

    return { temp, heated, switches, coldest };
}
```