```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) || !Number.isInteger(power)) {
    throw new Error('Start, low, high, and power must be integers');
  }
  if (low >= high) {
    throw new Error('Low must be strictly below high');
  }
  if (power <= 0) {
    throw new Error('Power must be a positive integer');
  }
  if (!Array.isArray(drifts) || drifts.some(d => !Number.isInteger(d))) {
    throw new Error('Drifts must be an array of integers');
  }

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

  for (const drift of drifts) {
    if (temp < low) {
      temp += power + drift;
      heated++;
      switches++;
    } else if (temp >= high) {
      temp += drift;
    } else {
      temp += drift;
    }
    if (temp < coldest) {
      coldest = temp;
    }
  }

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